Be careful with the use of the word 'beer.' The English mostly drink ales. I can recommend a couple of places for ales, but personally I cannot stand the atrocity. If you're particularly, morbid, give bitters and stouts a go. Prepare a plastic bag.
I base my choice of pubs by my choice of lager, but even then it's rather hard. It is difficult to get good lager in London.
Typically, I drink Kirin Ichiban (Japanese), Staropramen (Czech), Erdinger (German), Estrella (Spanish), Blue Moon (American, from Colorado I believe), Kozel (Czech) and a few others. You can also get bottled beers on top of these.
As these are import lagers, they go for 4-5 pounds a pint.
If you want something more affordable then particular pubs have exclusive distribution agreements with a particular brewery, these are called the Samuel Smith pubs. They offer Wheat Lager, regular Sam Smith lager and some other stuff, all of which are quite affordable, going for ~2.80-3.50 a pint. I live in West Central so that's the area that I know the best. If you plan on frequenting, then I can give you tips on some great places.
As far as cocktails go, you cannot go wrong with The Lab:
http://www.labbaruk.com/
The cocktails there are simply sublime. I'm a huge fan of Zombies and you can get very, very good ones at the Lab. They also do a special Zombie, which they claim to be by the original recipe (which is supposed to be lost).
I quote their menu:
Don the Beachcomber Zombie "The Big Boy! A heady mix of five rums, Pernod absinthe & maraschino liqueur with fresh grapefruit & lime juice, balanced with a dash of grenadine & velvet Falemum. As the Don said, "Only two per customer!""
It's well worth it, but rather pricey at 18 pounds. Anyway, every single cocktail that I've tried there has been absolutely amazing so you cannot really go wrong.
If you're looking for very classy places then Sketch also has fantastic barmen.
http://www.sketch.uk.com/
The Sketch actually consists of two restaurants and about 2-3 bars and a club. It all fits in rather well and it's a very stylish place. Albeit a bit pricey. And queues on Friday and Saturday evenings can be long.
If you're looking for pubs with a bit of history then you can try The French House. There's a long and interesting story behind this place:
http://www.frenchhousesoho.com/
They serve only half pints of beer, as used to be the tradition. They also have a smashing and very affordable wine list. Also, the food is top notch, they offer a wonderful blend of pub + French food at a very reasonable price. If you're planning to eat, aim to get there well early, preferably a bit before they start serving.
Anyway, that's just the surface of it really! London is a fantastic place for a holiday!
edit: oh yeah and as far as bars and pubs go MonstaMunch is spot on. In a pub you drink beer or wine (if the place is respectable enough) and you can also drink simple stuff like spirit + soft drink / juice. Shots are always welcome.