For Indian food, have a look at London's Michelin starred Indian restaurants. The Cinnamon Club does a set lunch that's a good value, and Gymkhana was amazing. There are more. I wouldn't recommend Brick Lane for food; atmosphere, possibly. Or for a different price point and take on Anglo-Indian food, have a look at Dishoom (very fun and very tasty).
Iconic means different things to different people. Some ideas would be Rules, Simpsons, Sweetings, and J Sheekey, for places with history. Or you might want a Gordon Ramsay or Heston Blumenthal restaurant, or not. One of the Ottolenghi restaurants?
The Ivy is iconic in its own way and I can recommend the shepherd's pie (there is an outpost in Covent Garden).
If you want a blow-out afternoon tea, Claridge's, but you'll pay for it. Iconic as it is, I'd skip the Ritz.
Or for modern iconic for steak, Hawksmoor. Or for modern iconic for British nose-to-tail, any of the St John locations. Or for modern iconic for Mexican, Wahaca. Or for modern iconic open 24/7 with possibly a view if you can get a table, Duck and Waffle. Or for modern iconic for a pizza chain, Pizza Express. Or for modern iconic for a market, Borough Market. Iconic can cover a lot of territory. Maybe you can tell us more about what you want.
Hot Dinners is a good website to get a feel for restaurants and chefs and food in London. Chowhound is not as active as it once was.
But there are so many excellent restaurants in London that it would be hard to name any MUST try places, without an idea of budget, location, and food preferences. Maybe it depends on what you can or can't get at home. As you're not travelling for a year, there will be great new must try places by then. If you're reasonably selective, you can eat very well in London.