According to The Global Language Monitor there are currently 1,025,109.8 words in the English language. Shakespeare himself invented 1,700 of these. When considering where best to study English, history, culture and most certainly literature should be included in the decision making process.
With this is mind my first pick for the best places to learn English in the UK is Shakespeare's Stratford-upon-Avon. Stratford-upon-Avon College is a good place to enquire first.
Here you can really soak up the literary culture and history that Shakespeare left behind. The town is a manageable size for those not too interested in nightlife and all the trappings of a modern day metropolis. There are plenty of wonderful old buildings to visit, including of course the residence of the great author himself.
London has more schools and universities than any other city, more to see and more to do. However it also has more people, crowds and traffic. It can become overwhelming if you are not careful.
Also prices can be extortionate compared to the rest of the UK. Nevertheless if you want options, London has a great many educational institutions to choose from. It also has many communities from countries around the world, which can offer a much needed social support network for many first timers in the UK.
If the bright lights and high prices of London seem overwhelming, a happy medium would be Manchester. This is a city rich with history, culture and nightlife. It lacks the immenseness which can make London overbearing sometimes and it is certain much cheaper.
Manchester is known by many to be a friendlier alternative to London too. At least one Manchester English school I know of gets rave reviews for being a more laid back and friendly place than the often larger institutions in the capital. I found that my time studying in London meant miles to travel between classes and rarely the same people in different lessons.
If you are still unsure look up the Wikipedia and Wikitravel pages for each place. They can all easily be visited in a couple of days by train if you wish. See the locations on the map below: