Do pubs or restaurants offer happy hour with reduced price drinks and appetizers such as we experience in America? If so, I am open for recommendations in London.
I don't think I've seen a Happy Hour offer anywhere in the UK for donkey's years. You'd see it quite often in the 90s (except, as Emma says, in busy areas), but it seems to be one of those fads which has been and gone.
Avoid cocktails during happy hour... I'm convinced you just get one cocktail split between two glasses. Beers, Wine, etc. are fine, because it's easy to see what you're getting. I personally try to avoid places with a 'happy hour'.
Some places do 'buy two large glasses of wine (250ml), get the bottle (750ml)', which can be a good deal.
In general... it's rare.
There is now a legal restriction in England that alcoholic drinks may not be sold below their cost price ie duty and VAT. This restricts the scope for price promotions without removing them altogether particularly on such things as weird cocktails full of leaves served in jam jars where the alcohol content cost is a mere fraction of the price.