Borough market to start... delicious food from regional farmers/butchers/producers etc.
www.lfm.org.uk/index.asp

also.. Berry Bros and Rudd.. i've never been, but hopefully will on my next trip down to london
www.bbr.com/GB/wine-know.../tastings.lml

There are tons of celebrity chef restaurants in london as well (and i'm sure they'll all have some excellent wines to offer) but i'm sure that's the first place you'll find if you ask for a 'slow food restaurant' is jamie oliver's fifteen - it gets mixed reviews so i'd beware. i'd try The River Cafe first myself.

But london like any other city is FULL of run down old cafes that make the best food you could ask for- don't be afraid to try them! (actually, there's one around the corner from borough market that is amazing)