L'Atelier/Joel Robuchon upstairs or Pied a Terre might work although pricey.

Yeah thanks but pricey is not on our menu. We need to be able to actually eat the food and not choke on it while seeing the prices. LOL

While it is in adjacent Marylebone, the Golden Hind was a wonderful, affordable choice for a delicious and traditional fish and chips meal. It's BYOB, so pop by a drug store or market beforehand and grab a bottle of wine or beer--they will happily uncork for you. It's a great meal, and an excellent value, in a town that doesn't offer a ton of great values for dinner!

We ate in a very small place called le Bistro Savoir Faire at 42 New Oxford Street. The food was excellent, and it was not expensive. You might need to make reservations; you can look it up on line.

Consider North Sea, though I'm not sure what "save seafood (although fish is excellent)" means.

http://www.northseafishrestaurant.co.uk/

Great fish, quiet surroundings.

Da Paolo in Charlotte Place, just off Charlotte Street is an excellent Italian restaurant, not sure how quiet it would be on a Friday night, but they do have a basement area which might be quieter than upstairs.

http://www.dapaolo.co.uk/

"not sure what "save seafood (although fish is excellent)" means."

"save" in English, when used as a preposition, means "except".

Finding a quiet restaurant in central (or any other part of) London on a Friday night is tough, going on impossible. I've never in my life found a decent fish & chips place meet the "quiet" criterion on a Friday night, for example.

With your criteria, I just wouldn't eat in a London restaurant, unless the budget stretched to somewhere where it's possible to book a private room. Since you don't have the option of someone's house, a hotel dining room is probably the best bet. No idea of where to recommend (who'd eat in a hotel, except for quiet?): use the selection tool at http://www.timeout.com/london/restaurants/, set it for Bloomsbury, then after it's selected, reset the filter at the top right of the results to 0.75 miles.

Read the reviews carefully, rejecting those attracting giveaway phrases like "popular", "party spirit" and the like.

This place (www.thebullsteakexpert.com) I remember reading a decent review of that included a reference to half-empty, which is what you want. Don't see the point of steak, so can't comment.

Though very busy, this place (www.asadal.co.uk) was astonishingly quiet, does have private rooms and a very reasonably priced set menu and I found both excellent food and charming staff. Though its street address is High Holborn, its unprepossessing front door is next to Holborn tube station on Kingsway. Don't be put off by the brusqueness its staff display on the phone.

My confusion is not with the word "save" but with the apparent exclusion of fish from seafood.

Thanks everyone for your replies, I am checking all of them out. I regret the confusion I caused with the fish and seafood. I meant that we eat fish but not : lobster, shrimp, mussels, and the like.

You can also check out top table for recommendations www.toptable.co.uk some of the reviews might give you an idea of noise levels? You could also try a curry place, they never strike me as loud like some of the trendy places do.

Update - we are back and ended up in Norfolk Arms right near our hotel. It is a lovely place BUT BUT BUT :
1) even though we had a table on the upstairs floor where it is indeed quieter and smaller (only about 6 tables I think) it was still a bit too noisy.
2) Service was NON - EXISTANT. Really and truly it took ONE HOUR for the waiter to even come and TAKE our orders.
3) and food was mediocre at best with too high prices.
Oh well.

On the other hand, we ate VERY well at Balfour Italian also right near our hotel. Good fresh food, friendly atmosphere and service staff, reasonable prices.

Also tried North Sea Fish, also happened to be right near hotel, and agree BEST fish and chips ever. Yummy.

Other places we ate : take out at Pret a Manger - a fabulous chain sandwich, fruit and others place highly recommended for a light meal. Really great.