I hesitate to post this as its the kind of place I wouldn't want to see ruined by hoards of chowhounds. But I'm thinking its far enough out of the tourist sections of town that only cheap fools like me would go. I've eaten there every time I've been to London for the last 30 years and last time I went (2 years ago) it was better than ever.
Vijay, next to 47 Willsden Lane, in London (Kilburn). You can catch the #99 bus going to the "Willsden Lane Bus Barn" on Oxford Street. Vijay is on a corner and the bus will let you off across the street. If you go past it you'll see a cemetery on the left.
Not surprisingly it's cheap -- four of us had everything we could eat and took stuff to eat on the plane the next day and it was about 50 pounds. The South Indian specialties are on the first page of the menu. Do try the Masala Sosai-a huge 14 inch lentil flour pancake filled with deliciously spiced mashed potatoes and served with Dal that has vegetables in it. Also have the Aloo Paratha which has potatoes (aloo) in it and comes with a fresh coconut chutney. And don't miss the Uthappam which is brown rice and lentil pancakes with tomatoes, onions green chilis and ginger.