I was in London for 8 nights back in early December. In general, prices on menus [in GBP] were similar to prices on menus [in USD] here in Los Angeles. With the exchange rate at the time approx 1.34, the premium in London is approximately one third more than LA prices. And of course, it's easy in London to cut corners, depending on how often you can abide eating at Pret, Gail's, etc. I made a deal with myself not to fret over prices when dining, and had meals at a variety of price levels. Traveling solo, I gravitated toward more casual places. Following is a sample of meals and costs - some readers may find this a bit tedious to plow through.
Breakfast - the buffet at the Novotel Waterloo was quite good, and at £21/$28 a good value, considering you can make as many cappuccinos you want from the machine, they had a good selection of fresh fruit, etc. and no discretionary service charge added. So with a big breakfast it may be possible to go most of the day with just a snack - or a cream tea - in the afternoon.
I found a cute neighborhood spot - the Rise and Dine Cafe - just down the street - and had several excellent breakfasts there - salmon benedict + cappuccino + pastry £18.85/$25.18, salmon with eggs on toast + cappuccino £15.63/$20.95.
Porridge + cappuccino + a croissant was £15.60/$20.96 at the very cute Beyond Cafe in Lambeth, while the same basic menu was £14.20/$19.07 at Gail's down the street [OK but not as good as Beyond].
Wagamama is a good choice for a relatively inexpensive meal in a lively atmosphere - dinner one night at the Southbank location was £30.60/$40.90; lunch at LHR on departure day was £30.47/$40.84 for ramen + drink - airport prices.
Flat Iron is an excellent choice for a relatively inexpensive steak in London - lively atmosphere and flavorful steaks - although not as tender as a £40 or £50 slab of beef. The £19 ribeye, with two sides and a glass of wine came to £42.29/$56.50 - make a reservation if going at prime times - you get a free ice cream cone as you exit.
After learning about JD Wetherspoon's I had to try it to see what you would get at those prices. I ordered a burger - how can they screw up a burger you might ask - well, it was just edible, but small, with some not very good chips thrown on the plate. This was the Waterloo Station location. £12.39/$16.65. If you're game, you might try them for breakfast - seems like a good place for a family to dine with kids. Semi-automated - you order on your phone after scanning the QR code at the table. I'm assuming they'll have robots delivering the food in the very near future, as is already the case in Japan.
Tea + Cake at the wonderful Tea House Theatre in Vauxhall was £13.50/$18.02 one afternoon. I also had a great breakfast there, but paid cash, so don't remember the final cost. But the ambience alone makes it worth a visit.
A not-very-good Sunday roast at the Hercules pub in Lambeth, with drink + dessert, was £48.99/$65.81 - not my first choice, as the gastropub down the street that I had intended to try was closed for a private holiday party.
I had a cheap snack at the cafe at BFI Southbank - £9.70/$13.03 - it was a good value. However, food at the British Museum I found to be rather expensive - £15.00/$20.01 for sandwich + tea. I found the cafe at the Tate Britain to also be pricey - so the free admission doesn't necessarily mean a cheap visit.
It's easy to get an idea of prices by reading menus online - for example, Dishoom appears to be a good value considering the rave reviews - it was on my list, but scheduling never worked out. Another thing I believe I observed was that some places included tax in their menu prices, while others tacked on the tax at the end - perhaps one of the Brits could comment.
But there are so many choices in London at so many different price points that you should be able to consider yourself well fed without extreme deprivation if you're traveling on a budget.