You need a fair bit of skill or luck to find, select and acquire a fine old bike at cut price, and to know how to kit it out for pennies. I did that with my London commuter bike mainly to avoid tears after theft.
I think it's patience more than anything, I've bought several high quality but silly cheap machines, each time watching a lot of overpriced examples and molested junk and just sat on my hands, waiting for the right one. My Royal tourer took over a year to turn up. It's not perfect but it's way better than I've any right to expect it to be for £30!
I've never had quality bargains from Inner London, just cheapo fixer-uppers. All the nice stuff has come from the outer fringes or around the M25 outside of London. The wealthier the area, the better the condition with less signs of high mileage, often one owner from new. It seems a bike from the middle of London will either be good but expensive or it will be hard-used and tired. I've never found a good but cheap one, probably too many people who can't drive all searching for bikes within a small geographic area. I suspect a lot of well-off people in the leafy, pleasant to ride in areas bought some quite pricey bikes in the pre-internet era, because their budget wasn't tight but then never actually rode them that much. Those bikes reappear during garage clear outs or because someone has given up riding due to age, and there is usually nothing much wrong with them beyond having flat tyres that have seen better days. Sometimes they look to be 100% original condition, like nothing has ever been replaced in over 30 years, meaning low miles and a lack of hard use.
