Discounting property prices, my cost of living in London is cheaper than family who live in the north. I do not spend thousands running a car, I have a wide choice of local chain and independent restaurants and supermarkets charge the same price nationwide. I rarely visit pubs which is the other noticeable difference.
Property and transport prices are the killers in the south east, definitely. If you don't have those, for whatever reason, then in a lot of cases there's not so much difference. There is a difference though, my experience is the supermarkets down south put 5p-10p on a lot of items, just not the staples (bread, milk, etc) that people really notice. It makes sense, staff wages are higher and that has to be paid for. Tesco charge more here than in the north east because of their additional transport costs, which again is fair enough really.
Pubs, as you say, and restauarants depending on where you are and whether you pay the "discretionary" service charge which always seems to be 5% higher than up north.
That said, when I lived in Muswell Hill a fish supper from the place on the Broadway was about nine quid, it wasn't massive, and that was six years ago now. I also can't get away with the southern chippies leaving the skin on.