Pricey - but excellent (and very good for pairing food with wines)
http://www.roussillon.co.uk/ (near Sloane Square tube)
Isn't exclusively vegetarian but offers some exquisite vegetarian menus - It is just possible they could cater for vegans if you gave them a call. Their current MENU LÉGUMES consists of:
PAIRING OF SEASONAL INGREDIENTS
ARTICHOKE & PEAR ~ CHERVIL & SHALLOTS ~ BUTTERNUT SQUASH & TARRAGON ~ PUMPKIN & PARMESAN ~ SALSIFY & CURRY ~ CHEESES & QUINCE ~ PEAR & WALNUT ~ CLEMENTINE & ORANGE
(Lunch here is best for value - 3 courses and a half bottle of wine for 35GBP)
EDIT TO ADD - found out recently that this restaurant has a Michelin star

Near me there is
http://www.manna-veg.com/
(just North of Camden) not quite as refined (or expensive) as Roussillon but certainly recommended
The location is next to Primrose Hill, it's a park that's often featured on TV and in movies as it has unbeatable views of the London Skyline.



Not upscale at all: For one of London's real hidden gems, have lunch here:
http://www.museumgardenhistory.org/
(near Westminster, on the other side of the river - or walk there along the Thames from Waterloo)