How to get good

A good way to start would be to chose some 'primes' on your route. Tradition would dictate that these would be the tops of hills or the town boundary.
But practicality would suggest a feature that you can see from some distance away that will not move (so not a dead Badger) in an area where you can ride as fast as you can.
Again the 'sprint' should last 30 to 60 seconds and don't get into a routine.
Imagining you are riding down the Champs Elysees on the final stage with Cavendish chasing you down optional

Looking forward to my intervals complete with rucksack, rack & pannier tomorrow morning, best get my head down!

Lots of good advice but I would also suggest an hour or two per week of pilates. Strengthening my core really helps and I find gets good results quickly. No matter how fit you are you can always improve core strength and it will feed through into more power/speed.

EPO!!

Keep it fun! Structured, formal intervals are "horrible" - soul destroying - leave them to the racers. Make your "intervals" what you want them, just ride harder than you would normally go for a bit. If it's windy do some of the efforts with the tail wind and get to feel "fast."

Other times if you're feeling strong do them uphill or into the head-wind - just keep doing a variety of efforts above your normal speed. Give yourself time to recover, then go again. And as above - stop before you're knackered. 45 mins max, then finish with a gentle potter home in a small gear to ease the legs off.

The runners call it "fartlek" - speed-play. It's what kids do when they get a bike. Keep it fun and you'll look forward to it and enjoy it - and get faster!

As others have said, joining a club will get you fit fast. Your technique will improve (maintaining speed better through corners and knowing how to climb will boost your average for free) and having faster riders to train with will naturally make you push harder. Riding with others quickly taught me that I could push a lot harder than I thought was possible, and that's great for getting fit fast.

I went from pretty much unfit with say a 15mph solo average when I joined my club at the beginning of the summer to about a 19mph solo average now (not too hilly round here). Don't worry about being passed by a group, we can easily hit 25mph on the flat in a group ride, I'd be dying if I tried that for any distance solo!

Stop worrying, keep riding. Simples

What do you want out of cycling? Faster commute? Be better on hills? Train for long sportives? Road racing / time trialling?

If you want to ride in a group and socialise, mix with other cyclists or just benefit from others' knowledge and experience then you really should find a club, or at the least a group of like minds near home.

If you prefer to ride alone (as I do) that's fine too, though don't dismiss club membership as being an in-crowd or cliquey thing. Most clubs are not like that at all.

Oh and don't worry about the speed the group passed you at. The difference between riding on your own and riding in a well-drilled group is incredible, it's an extra 5-6mph without even trying. If they're gunning it, it can be an extra 15mph!

Hi dunnoh, our club regularly passes people at speeds such as you describe, but honestly, the bulk of that is momentum built up by the group. I sometimes feel a little sorry to see a guy plugging away on his own then hear 'passing on your right!', only to be overtaken as if he was going backwards... I certainly don't ride at those speeds on my own!

16mph avg is fine to join most clubs, and is in fact what I'd probably achieve on my own. The social groups will go slower, the racing groups will go quicker, and somewhere in the middle you'll find what you're after. It takes a few weeks to get used to the pace and holding wheels etc, but all good fun.

I've started commuting recently. Only 2 days a week at the moment, as I can work from home for the other 3. This is how I do it:

Wed morning: Rucksack & pannier, pretty quick for the 7 mile run, focusing on a powerful pedal stroke with all the additional weight I carry.
Wed evening: Leave the rucksack (laptop) in work so pannier only, extend the commute to 18 mile loop (may extend further), make big efforts on hills.
Thur morning: Extend the commute to 18 mile loop.
Thur evening: Rucksack and pannier, focus on powerful pedal stroke again but absolutely give it the beans on the sections of road where safe to do so.

Sunday: Long steady ride, currently building back up to rejoin club runs after an injury.

Other days, core strength, gym or whatever else I can fit in.

losing weight very slowly is the key, that way you can always et properly which you need to do to perform well.
Your frame dictates whether you will ever be a lightweight, but most weekend warriors could lose a few pounds

Totally agree with SideBurn,if you lose weight try not to lose power.also gain leg strength with running,squats etc.dont worry too much about hills as nearly all amateur cyclists aren't built like a Froome or Contador.most cyclists are more like classics rider

7 hours is doable, it just means you will be most adapted to going quick for an hour or 2.
Three 1 hour long proper hard rides and two 2 hour steady (not easy) rides would be your best bet I reckon.
Personally I would leave the turbo for now. I use mine a lot, but only because I am goal driven at the moment. I would not touch it with a shitty stick if I was just starting and generally trying to get quicker. They are hateful.

You sound similar to me when I first got going, focus on having fun but trying hard. You dont need too much structure yet.

I am kind of at a similar stage myself.

Most clubs have groups to suit all abilities and development/beginner rides that don't drop people and stop for mechanicals etc. I have been doing that for six weeks (40 miles at around 14-16mph) at the weekend with a cycle commute each day plus one evening a week a 12-20 mile hilly route and have noticed some improvement. I vary the commute as its very short to incorporate a couple of short climbs.

But group riding has been key for me and you get good advice and tips from those you ride with.

I went from being tentative and full of trepidation on my first group outing to it being the highlight of my week. So in short go along to a club beginner group ride. You won't look back.

Losing weight is a good way to improve your power to weight ratio which will help -a lot- on the hills. But it is difficult to lose weight without losing power as well.
A good training regime will have speed, strength and stamina sessions in it. To increase your speed you need to focus on interval sessions (short hard sessions) and strength sessions (weights or hills).
You sound like you have the basic stamina that you need, joining the right club will improve your ability dramatically.

You didn't say how much cycling you're doing but you're not going to get fast if you're not willing to invest your time.
8-10 hours a week (annual average including winter, bad weather, holidays etc...) of riding would be a sensible target but if you have less time available then you need to crank up the intensity of your rides.
Extending your commute would be the most time effective way of getting more miles in.

If you want to get quick,
First have a look at how much time you can spend on cycling. Work out the most time efficient way you can do it and how much you want to do it. Can you squeeze rides into lunch 'hours' I get up at 5 a couple of days a week and jump on the turbo or it gives me more hours in the weekend to get a long ride done and still have time for everything else.

Once you have a realistic number of hours (some v v quick people do less than 10 hours a week) divide it up into a few rides that really push yourself of an hour or so and a few that are still effort, but sustainable for 2-4 hours. Have at least 2 days off a week. If you have few hours drop the longer easier stuff and focus on being well rested for the hard stuff.- Maybe get some miles in for a few months first, it sounds like you are new so try a few months of just riding as much as you can to get general fitness before going mad. Once you start doing the shorter rides try to find a loop where you can measure improvement over time.

But do whatever is enjoyable for you. It becomes a chore for some. I love pushing myself though and would nor ride without a competitive aspect (even if it is just against myself a lot of the time)

I was in a similar position to you I think, felt generally fit and did quite a few miles including a commute, but wasn't getting any faster. Preparing for a sportive I borrowed a turbo trainer and started looking for bits of my commute where I could safely do properly hard sprints, and in just a month or so I could hold a higher average speed and turn over faster too. It doesn't necessarily take that much more time either, certainly compared to 60 hilly miles (know which I'd rather do though). I also got hold of a heart rate monitor to keep an eye on how hard I was working.

So one answer might be some boring, hard, repetitive interval training, maybe on a turbo trainer. In his book Graeme Obree talks about the difference between "training" and "just riding quite fast for a long time"; one of the differences between serious sportspeople and the rest of us is just how hard they're prepared to work. I can't remember the last time I had to stop and throw up and then do ten more sets of whatever horrible thing I was doing.

It's true what others have said about making sure you still actually enjoy riding your bike. If you stop looking forward to it you just won't go out, and that's no fun. But doing some short intense intervals will probably help.

Why worry - you are mixing up basic cycling for transport with leisure/sport riding.

Many find averaging over 10-12mph ruins the enjoyment of a bike ride, where you have the ability to stop, look, and communicate with local people as you travel.

As for special kit - I don't own a scrap of fancy technical clothing, unless you count Harris Tweed

Just build up speed over time.have you a cycling computer/garmin etc.try and better your time commuting,try knocking a minute off every few weeks.what is your average speed?

You shouldn't compare yourself to the group that passed you. You've no idea how long they had been out, where they had been or what their racing category might be. They also benefitted from the aerodynamic advadtages of group riding that you just don't get on out on your own. Stick with what you are doing, losing weight will help and inevitably follow from your lifestyle changes if you keep a lid on your diet. When you feel like it, push on and add some intensity to your rides, don't bother when you are not up to it. Lots of people find the competitive aspect of Strava enjoyable and a source of inspiriation for pushing themselves a bit harder. If you get the chance to join a group ride then that might help too. Set yourself some realistic goals like adding 1mph average speed to a familiar route and see how you get on. If you can hack 60 miles in the Peaks you are already well on the way to getting good.

Good luck with your riding.

join the club they will look after you and eventually you will have enough speed and miles to enjoy a club-run