Non-independent stores in the UK that sell manga
I would suggest checking if you have a local forbidden planet, they have locations all over the UK and always had a wide selection available; their website is here http://www.forbiddenplanet.co.uk/

I found most book stores generally have a small manga/anime section. Depending on what exactly you are looking for you may do better looking online, the best site in my experience is http://www.bookdepository.co.uk/ which returns over 100,000 hits when I search just on the word manga. 

There are many other online options which you can find using a search engine. 

I hope this helps.