My favourite place in London is Le Gavroche , small dining room, attentive service and exquisite food. I would say it is quiet, as in not boisterous, but obviously people are talking at the tables and having a good time. Excellent value lunch M-F (although I've never managed to go). Dinner is expensive (c. GBP100/ head and up).
However, I would agree with many of the recommendations above, although not all of them would be world-class cuisine, but perfectly tasty.
tb