Well that's not really a focus of British culture traditionally. The main people who want to drink cocktails are people going out clubbing. The main traditional drinking places (pubs) serve mainly beer, cider, and wine. The situation is similar in Germany. That said, in the UK with the "plastic pubs" it is now way more common to be able to get (bad) cocktails anywhere.

Though one experience I will never forget going into a fancy bar that opened in my mum's small town and asking for a martini and the bartender looking confused at me and serving me a shot of pure unchilled vermouth in a near-empty tall glass...