I'm going to argue for buying another bike. It sounds like you want to ride a bike not learn how to fix one.
Repairing bikes has costs parts tools, a bit of grease, chain lube paint can soon add up also your time. What's your time worth on an hourly basis ? £10 any hour ? More ? It all soon adds up. Say, maybe it dosen't come together ? Then you've got an expensive pile of bits in the corner that isn't a usable bike.
Surley much better to buy a new or second hand one. Sell the Peugeot to help fund the project, so that it becomes an asset not a liability. There are plent of single speeds from cheap to expensive as well as plenty vintage bikes out there. Lots of choice of ride home stuff about without the stress.
Just my thoughts, I wish you many happy miles.