Chain falls off more since removing front derailleur

1000m is no distance unless you've neglected the bike. Which you might have. 

You need that front derailleur back. 

Superstar do these ones for cranks with 110bcd (which is pretty common)

Not toally infallible without also using a clutch rear mech, but potentially a fairly low cost and neat solution.

http://www.superstarcomponents.com/en/cyclocross-io-chainring-narrow-wid...

Do they do Thick-Thin chainrings for road bikes. This, along with clutch derailleurs, has enabled mountain bikes to go single ring for a while now.

"the chain now comes off a lot more than it used to do"

Step 1: Measure, if you don't have tool, for chain stretch with a ruler. https://www.youtube.com/watch?v=5okJdYrANt8  Skip to 1:27 . A worn chain equals a dropped chain.

Step 2: Ensure you have the correct chain length. Too many links will cause chain drop off chainrings. Even one extra link will do it.  http://www.parktool.com/blog/repair-help/chain-length-sizing

Step 3: Ensure you FD is at the correct height so the cage upper prevents the chain from bouncing off.

There is a good reason why downhill bikes have chain 'devices' to keep the chain on... Unless you are going to go singlespeed you will need some form of chain device. You are using a chain and chainring designed specifically to allow the chain to drop off (and on) efficiently. You will notice the chain comes off more often when the chain line is less than perfect (it will only be perfect on one of your rear gears). Even with a new chain etc you will not stop the rear derailleur tensiong and de-tensioning the chain over bumpy surfaces. As you are only using the bike for commuting I think the best option is a cheap basic front derailleur. There is no need for a cable or shifter. Use the limit screws to align it to work best with your five rear gears.

You are a very naughty man, Mr Manc, to let your bike get in such a state.  It is a legal and moral requirement that a bicycle is maintained to be 105% cleaner than it was in the shop.  But, as you have confessed, we will forgive you and look at your problem .....

Could it be that your chain is rusty, dry and, at least in part, rigid?  If so this would explain why, without the front derailleur to control its position, it regularly tries to leave the bike.  Nothing there that a good clean and lube won't sort out.  Maybe even a good soak in a light oil?  And there is a chance that the rear derailleur isn't operating to keep the chain tensioned.  Maybe this too would benefit from a good clean and lube?  These tips are free so try them first.

And it's true that a very worn chain will tend to misbehave.  Your history of inaction with the oilcan suggests that it may, even at low mileage, be stuffed.  But chains are cheap so that's easily fixed.  But they aren't free so try this second.

There is also the chance that your cassette and chainrings are showing signs of your woeful neglect.  These are far from cheap so this should be lower on your list.

Finally, if all else fails and you are reaching the point where the bus seems a good alternative, you could fit a chain tensioner.  They seem to appear regularly on eBay for little money but aren't expensive from the shop.

Best of luck.

I would suggest that the chain needs replaced. Though after 1000 miles I wouldn't have thought so unless you were constantly in the 'granny' ring which would have exacerbated wear. I usually get at least 7/8k on a chain. Meanwhile my single speed I can't remember when I replaced the chain. 

have you also checked the rear mech and cables aren't seized either? If you don't have the correct tension there, this could be why you're throwing your chain.  Also check your chain ring for wear. I'm assuming that you're always using the small ring at the front.  If the teeth are wearing down then there's nothing to grab the links.  Start with the chain for definate.  

Anything that would help keep the chain on would probably end up being a similar price to a cheap front derailleur. The chain sounds like it might need replacing as well.

Not sure there is a cheaper option that will work well.