Yes the supermarket thing is confusing me as well. I dont recall really ever doing big super market shops, even when the kids were younger. Independent butcher, baker, cheesemonger ,and fish and fruit from the market.
Better quality and overall much cheaper and healthier than being tempted by supermarket "bargains". Then the odd top up from (the many) nearby small supermarkets, and some bulk buying of cleaning stuff when passing a Lidl.
Maybe part of the art of enjoying life in London is to start living like a Londoner. Many of my friends have always managed fine without cars, and if I did not jhave to make regular trips outside London it would not be worth having one.
Edgy to me means somewhere where you might feel obliged to pick your teenage DC up rather than have them return home from a late night party using a night bus. Or where you clutch your handbag tighter when you walk down the street. I feel as safe where we live as I would in most towns in the UK, and DC always used public transport without me worrying about them.
I still have not worked out where you live, Bubbles, but from your local park with open drug dealing etc, it would definately fall under my description of edgy. Edgy areas can be fun, with lots of stuff happening, and relatively cheap, but it depends on your attitude to risk. Many people prefer to pay a bit more for a greater sense of personal safety. There is a continual regeneration in London where young people move into cheap areas, "fun" bars and cafes follow them, and then the next generation are priced out and colonise somewhere else.