Logistics to going to LCB London?

I am a future culinary student and I have fell in love with what LCB has to offer and also the city of London and the the UK, it is where I see myself living in the future. (from the USA) I am starting to plan out my future and part of that is going to school there. So I was wondering a few things.

1 living: I know that living in London is one of the most expensive city's to live in Europe. So I wondering what living there is like, for example is it possible to live in cheeper neighborhood that is a bit farther away from the school and then take public transport to get there. this leads into my second inquiry.

2 is working while going to school. does anyone know if it is possible for someone to goto school there and also work at the same time, it is 100% necessary to work to minimize my loans I will be taking out I would like to only take out loans for the school and pay for the rest out of pocket. My family can afford to send me to school (let alone LCB) I would prefer to not take out a lone to also cover my living but I also want to get as much as I can from my time at LCB because that's why I will be there.