London next week, upscale but not high end nor set menu

We are a family of four from San Francisco including 16 & 19 yr old girls staying at The Soho Hotel for 3 nights. Prefer a place which takes dinner reservations & has a la carte menu due to shellfish allergies. I realize I'm a bit late with reservations but appreciate your help.

Was unable to get res at preferred times at Gymkhana, Nopi, Palomar, Honey & Co....will try to do lunch. Trishna menu didn't excite me.

Aware of Dishoom, Barrafina, E Pellici, Borough Market

Looking for good food (not too gamey, lamb we love) in convivial atmosphere. Had Gordon Ramsey down based on friend's suggestion but balked at combination of $$$$ and mixed reviews here.

Social Eating House?

Thank you.