There's plenty of stuff that's British that isn't just edible but actually quite delicious. Most of the dishes I can think of are, however, somewhat time intensive and therefor not easy or cheap to come by when dining out.
Pretty much everything is quite expensive in London, though. That's just how it is.
Enter a bakery or other local small shops in the neighbourhood. Stay off the tourist tracks, if possible. Resist temptation of street food and omnipresent fast food offerings (except maybe some chosen samples for comparison with the crap sold at home, if so inclined). Expect the unexpected.
If you're into Indian food, you should check out Khan's, 13-15 Westbourne Grove, London W2 4UA - it's quite a bit away from your posh hotel, though. http://www.khansrestaurant.com/
What's closer is, say, Camden Town which is also worth a visit. Discover it on your own on a leisurely, majestic stroll of the tall man or use the power of Greyskull Google or some guide.
If you're into beer, http://www.ourblackheart.com/ - plus: home-made burgers.
If you're into fun underground deathtraps, I heartily recommend http://www.theunderworldcamden.co.uk/ - on the 6th, it's obviously Afghani folk music night: Bonecrusher Fest 2013 feat. Job For A Cowboy
Plus Beneath The Massacre + War From A Harlots Mouth + Gorod + As They Burn + Make Them Suffer.
There are splendid, tiny breakfast places around, look for those with lots of customers. If you're not queasy and nit-picking, go either for an 'everything' plate to get the full experience and caloric intake or just eliminate stuff you really, really can't imagine eating. I think a proper breakfast beats posh hotel breakfast with empty croissant calories most of the time.
An American that uses metric units. I am intrigued.