Saddle sores

The pashley is an upright bike without drops
The horizon is a touring bike with drops

The horizon has a Selle Italia FLX saddle and the pashley probably has something like a Brooks B67

Basically, in terms of the contact points for the two bikes it's about as unalike as possible

Also if you are putting too much weight on your hands the bike might be too long, maybe you have the wrong size

Stuff you could do:

Raise the bars on the horizon, possibly by getting a cheap adjustable stem

Drop the nose of the saddle on the horizon slightly

Pedal harder. This will move weight off your backside and hands

Maybe you could examine the angle of the handlebar grips as your palms meet them. Just rotating the bars will give subtle changes in angle which may ease the pressure on (for example) the heel of your palm.

Good on you, and kudos for doing it on a Pashley. The Ridgeback should be a good choice.

Saddles are a personal thing. I couldn't get comfy on the stock perch on my Giant SCR road bike but I've tried two Specialized BG models (both MTB saddles as it happens) and a WTB Devo and all 3 have been an improvement. I bought them all secondhand on ebay so didn't splash out much in case I found they were no better.

Padded shorts (with nothing underneath) are a must for any distance. Swap them regularly as clean shorts and clean skin are essential to avoid sores. Lusso shorts are good value, High on Bikes were selling the basic 6 panel for about £14 and the Pro 20 for a bit more the last time I looked, again on ebay. I wear Endura coolmax undershorts beneath my Altura cruisers as I prefer this to lycra underneath the tights, and no bare knees below 15 degrees. Apply Sudocrem daily, either to the skin or the pad of your shorts. Branded chamois cream (Assos, DZ etc) are effectively the same thing but cost more.

I often ride without mitts. Although they help, I suspect your discomfort may not be entirely down to the absence of gloves - it could be the way you're holding the bars or hoods, for instance. Also, have you tried running a lower pressure in the tyres? 60-80 psi is more comfortable than the rock hard feeling of 100+.

You may have realised by now that commuting by bike is not really a good way to save money. Once you start replacing or upgrading components, buy several sets of good quality cycle clothing and shoes plus a second bike for best and relegated your main steed to status of 'winter hack' the bank account is not looking so good. And that's before you get adding up the extra food you'll need! But I guarantee it will make you happier and healthier than putting £50 in the fuel tank every few days.

altura and endura both make good baggies with liners if you don't want lycra, the endura humvees are especially good

Simon, sounds like you're a middle aged chap mounted in comfort hiding an extra layer, or MACMICHAEL

if your hands are aching you definitely want to try adjusting your balance of weight, Stato's right. it sounds like a shorter/higher stem might help, and you could try double wrapping your bars or fitting tape with gel inserts.

saddles are a very personal thing but the Charge Spoon is worth a punt, it's (almost) universally liked and not expensive. you'll have no trouble selling it on if it doesn't suit

one other question: what do you wear to ride? if you don't have shorts with some kind of padding (don't have to be lycra!) and some decent gloves, then both those things will help a lot.

Obvious question, but are you wearing mitts? If not, buy a pair, close fit but not too tight with cushioning in the palm area, and you will notice a huge difference, particularly if you're covering that distance each day. I know I did after buying my first pair a few months after taking up cycling way back when.

Also, depends on changing facilities etc available to you, but if you're not wearing cycling shorts, think about it, even if you stick them on under a pair of longer shorts - I do (and as a result I'm unsure whether or not I'm a MAMIL. Maybe I belong to the covert ops unit)

If your getting sore hands and ar.. saddle then its possible your position on the bike is causing the issue. The pashley is a very sit-up position and the horizon a bit more stretched so consider taking it back to the shop and ask them about setting it up to be more comfortable, maybe raising the bars a touch or adjusting the seat. Of course it could be the type of saddle and grips that are casuing you pain, they are easilly swapped and there are a HUGE amount of options, so we can only reccomend what suits us and it may not suit you.

I run Ergon grips (they are made by a number on companies) that have support for your palm, lessening the pressure on your hands. For saddles a lovely Brooks leather model suit my posterior perfectly, and as they are common on pashley's perhaps they suit you too?

EDIT: p.s. Kudos on doing that sort of distance on the Pashley! good effort!