London is a very large, busy, industrious city, with lots of negative and positives. Let's look at some of them.
Negatives:
The rents and housing prices are MUCH higher than the rest of the country, they aren't quite a New York City levels, but they are high. One can expect to pay £90 per week for a room in a shared house or £180 for a decent one bedroom furnished apartment.
It's a very expensive city all round. The cost of getting into Central London in the early morning, is unbelievably expensive.
Positives:
Travel is easy and excellent quality and standard
It is the centre of England's entertainment industry making it easy to find something to do.
The educational and training opportunities are the best in the country.
You earn more, because you pay more for things.
It will be a more expensive life, but you will find yourself engaged with more.