I haven't lived in London for many years, so can't suggest specific places, but from memory and visits home can make a couple of suggestions:

Pizza Hut do a pretty good lunch buffet deal.

JD Wetherspoons pubs are family friendly and they have a reasonably priced menu.

M&S Cafe Revives are good (these are located within M&S department stores) - although they can get very hectic during the height of the lunchtime rush. Mainly sandwiches but they also do some hot options (soups, baked potatoes etc). M&S is also renowned for its tasty salads and sandwiches if you are prepared to grab a takeway from their food hall.

I've found it's worth checking out the cafe or restaurant in the museum or attraction you happen to be visiting. I've often been pleasantly suprised by the prices and food on offer. Many attractions will have a menu you can view on their website. Museums and attractions should not be overly crowded at the time of year you're visiting (unless you happen to be there during school holidays, which is usually two weeks around Easter).