Single chainring setup on a commuter road bike?

My wife rides a crappy Carrera road bike on her daily commute. It sports an Tourney/Altus front/rear mech, and when clean and freshly tuned, it runs pretty smoothly for what it is.

Her daily commute now involves a train journey - not really an issue, but it's one of those where you leave your bike leaning against the door and, every other journey, you hear fall over and, the chainset has an unsurprsing tendency to drop the chain whenever it happens.

There is lots wrong with it, as we haven't cleaned it for a while - I'm replacing the old chain and giving it a proper clean and adjustments tomorrow. I think it will improve things (the chain is visibly stretched and doesn't sit on the chainring well), but I want a better solution longer-term.

Should I:

1. Improve the chainset from the wealth of forum-provided options?
   
2. Switch to a single chainring?
   
   

The riding is pretty flat (London and Cambridge), so there is no real need for a front shifter, so I'm leaning to the second option - but then I have no idea how to best go about it. Top priority is to stop chain from dropping.

Ideas?

Cheapest solution would be a narrow wide chainring from eBay. Under 20 quid I think. Helps hold the chain a little better

Thanks Phil - I will start with that. If that's not enough, would a chain guide help further? Or a clutched derailleur?

Would have thought that the front der would help in keeping it on.

Third option- get a bashring to go on the outer spider- I run 1*10 like this with a normal (not narrow wide) chaining on the inside and it has been fine. Bash guard if sig bigger than chainring should make it harder for the chain to pop off outwards.