Actually I find that outside of housing, costs are often higher outside of London. Yes, there are some high end places that cost a bomb, but there are loads of cheaper alternatives thanks to competition. Where I live now the average price for a not very exciting main course is around £14-16. This is for food that they'd never get away with charging so much for in London.
Supermarket prices are the same, but street markets are better quality for cheaper in comparison to where I am now - thinking of places like Ridley Rd etc. There's also loads more bargain type local shops selling household goods and groceries, more plentiful and cheaper than in the provinces.
Bus travel is loads cheaper although the Tube is of course expensive.
There are deals to be had on theatre tickets, it's good value going to the Proms which of course runs all summer. There are loads of free cultural events, there are museums, great parks.
It's easy to pick up very nice clothes for not much outlay - markets, cheap little fashion stores, and for higher end places they totally slash prices at the end of the season because there's no way they'd put it out again - none of this five year old stock cluttering up the rails come January that you get in other places (with people, mystifyingly, queuing from 5am to buy it).
So on balance, discounting housing, I'd say if you look around and get to know where to go, you can have a richer cultural life for cheaper and also the nuts and bolts to keep you ticking over are cheaper too.