That's probably true of pubs, but if you want to go somewhere with a good cocktail or whisky selection, for example, it's very hard to find somewhere with low volume music.
It depends where you are. In Scotland it's hard to find a pub without a good whisky selection and in any UK city a pub will be able to make a wide range of cocktails. Having said that, some play loud music and some don't.
A pub may have the ingredients to make a wide range of cocktails, but most of them won't have staff who actually know how to do so well. If you're lucky someone will have had some training in making cocktails and be able to make something passable. If you're unlucky they'll grab the bottle of premix from under the bar.
Cocktail bars are a distinct thing, and have staff who actually know what they're doing, unfortunately they usually have exactly the same problems described in this article of being uncomfortably loud.
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...