Ok. So I am going to try and address everything you have asked for, then I might give you a few recommendations just based on recents that I have been to. With two small children, some of my favorite restaurants in the city are out (Mount St., Restaurant St. Barts, and Gymkhana to name a few), but there are still a lot of great places to go! I will list them by places that I have actually been, then places that are on my list to try, but I just have not made it just yet.
Indian:
Visited:I really like the Dishoom at King's Cross. I love the decor, and the food is outstanding (2017)
Unfortunately, the only other Indian places I have been in London are Bibi and Gymkhana (apologies).
On my list: The Tamil Crown and the Tamil Prince (one also does a Sunday Roast) - Both were booked up on my last trip, but my friend highly recommends both
Darjeeling Express (wanted to go last trip, but the wait was too long, which again, bodes well - The chef will do some Sunday tastings, which are highly regarded as well, so check that out)
Sunday Roast:
Visted: Harwood Arms - Fulham - Amazing Sunday Roast - you have to have reservations (2017)
Jugged Hare - City - Longhorn Rump Roast (dry aged, 40-50 days, so really tasty) - I cannot remember when I went, but I really enjoyed it.
The Devonshire - March 2024 Sunday Roast Visit - Really outstanding Roast - great wine too
Ladbroke Arms - Notting Hill ish - Went here in September 2023 - The pub is gorgeous and the food is solid
On my List: Audley Public House (I have been to the restaurant upstairs, Mount St., which is outstanding), The Constitution (I have been here for a beer, but never for food - They have an outstanding patio). The Grenadier (their Roast menu looks amazing)
Thai:
Visited: I have only been to Speedboat Bar in 2024. I loved it. Might not be great for kids as I went to the bar upstairs as it was later at night. However, they do have the more family friendly restaurant downstairs. Right in Soho in Chinatown - so a really busy area, but the food is so good.
On my list: Kiln (Soho), Chet's (further West), Supawan Thai Food (King's Cross!), and Kolae (Borough Market)
British/Traditional:
Visted: The OG St. John - I cannot remember when I went, but I had was so, so good (it was offal, and it tasted so so good), and I have been meaning to get back. Alas, my job has gotten in the way. But I highly recommend it. Not sure how adventurous your kids are, but I think they also have some normal stuff as well.
Quo Vadis - 2023 - Their pies are outstanding. I even bought the cookbook. Really historic restaurant with good, classic British food.
The Dove, Hammersmith - 2024 - Had an outstanding meal here. Yes, it is a pub, but it was so good. Everyone loved it. Right on the river, so a good place to go. Close to the tube.
Guinea Grill - 2023 - Awesome old school London chop house. In an old pub in Mayfair. Loved it.
Honerable Mention - Kitty Fisher's and Fallow (2023) - The chateaubriand at Kitty Fisher's is amazing
On my list: The Quality Chop House (was booked last trip), The Yellow Bittern (I think it is lunch only. Controversial (check out this article https://www.nytimes.com/2025/03/05/dining/yellow-bittern-london-restaurant.html - But I am already planning on trying to go on the 4th of July!), Sweetings (seafood lunch spot in the city that has been on my list for ages), M. Manze Tower Bridge - Pie and mash shop. Also, Rochelle Canteen - Fergus Henderson's (of St. John) wife is the chef and ower- been on my list, but hard to get out East.
Fish & Chips:
I always take people to the Laughing Halibut in Victoria. It is close to the office and it is really, really good.
I went to Golden Union in 2023, and thought it was also very, very solid.
I have passed by Hobson's in Soho, and have put it on my list.
Desserts:
Cedric Grolet at the Berkeley is expensive, but oh go good. pro-tip, order a cake to pick up, pick it up, and enjoy it at your apartment/hotel. We did that and took two cakes to Silverstone/Oxford with us. They were outstanding.
Peggy Porschen in Belgravia - Beautiful cakes and cupcakes. Recommend highly
Maison Bertaux - Never been, but it is on my list
Random Recs:
Wereworlf Beer - Sort of near King's Cross - A play on Werewolf in London - on my list to try out
Dim Sum Duck - Really good dim sum right near King's Cross. Tiny space - no reservations - I waited an hour and a half for it. I do not usually do that. Get there early (They open at 11), and the wait might not be so long. I went on Marathon Sunday. Bleh.
The French House - Pub with a restaurant upstairs - The pub is a literary haunt, and the restaurant has been on my list. It is country French cooking and the steaks frites come highly recommended.