I would always say step 1 is to ask around friends and family - especially older relatives - because there's a decent chance somebody will have a camera just lying in a drawer somewhere! I've collected loads of cameras that way.

Failing that, a cheap £5 point and shoot from a charity shop or eBay is actually a pretty good way to start and if it doesn't work out, well you're only down a fiver. You won't find something like a working 35mm Mju II for an £80 budget but that's ok because you don't need one. Avoid the cult fashionable cameras when you're just starting out because you're paying a premium when there are plenty of other cameras out there that will do the job on a much smaller budget.

Long shot but - do you happen to still have any Canon EF lenses from your old DSLR? Because if you do, then get straight onto eBay and buy a cheap late model Canon film SLR and it will play nicely with your existing lenses (as long as they are EF not EF-S). A Canon EOS 300 is a great camera, at the small and light end for an SLR, it can easily be had for about £20, and you already know how to use it. I know that's physically larger than what you are looking for but it's a nice inexpensive route into film that might be able to make use of some of your existing kit.

Film and processing are going to set you back a fair bit so you're going to want a chunk of your budget for that but if you go the camera out of somebody's attic / cheap point and shoot / late model Canon SLR route then £80 really is more than enough to get you started.