There are loads of ways to get a t-shirt printed in the UK, it really depends what you want though.
If you want a one-off print of a custom design then you can go to CafePress.co.uk and you can design it online and get it delivered to your door. The good thing about CafePress is if you create a popular design, other people can order it too and you earn a commision on each one sold.
Alternatively if you are looking for something a little cheaper then I would suggest finding a local t-shirt print shop. I live in a small town near Bristol and there is 2 here, so you should be able to easily find one in the area. If you are having trouble, find a local print shop and ask there as they are likely to know.
If you want to print a large run, for corporate clothing for example, then I would suggest finding someone online who specialises in that. There are many embroidery and t-shirt printing companies that exist, and they would be more than happy to do the order for you. Just search for 'corporate t-shirt printing' in Google