If you want cheap and cheap to insure, buy a skoda fabia. I think they're insurance group 1 or 2 and are basically a cheap Polo. Easy to drive, park in London and not too bad on motorways.
We loved ours and only replaced because we were doing more and more long journeys/UK holidays (and because I am a wanker).
We got our insurance down to about 550 a year (eb 3 years and me new driver).
Am also really enjoying our 118i now though and don't feel like it's too much car for me as a new-ish driver. I think the insurance is something like 800 a year and it cost just under 10k for a 2015 plate with 30k miles on it. Bought part cash, part small bank loan (better than ridiculous finance deals) so repayments are low and it doesn't cost us much to run.
If you buy a 2011-2013 one with less than 50k miles you're looking at 6-7k (fag packet estimate). I looked at golfs but they're a bit dull and pretty much the same money as a BMW so I bought the car I liked instead.