Way back I made a list whilst researching for EU t-shirt/mug places -- http://alicious.com/www-cafepress-co-uk/.
I've used https://www.tshirtstudio.com/ for mugs, they were good quality.
Most large towns in UK probably have a dye-sub printing place.
If you want cheap then Vistaprint is pretty hard to beat (cart abandonment usually nets offers).
I am looking at Qwertee and want to find out about their business model and designer compensation, but whenever I approach the page footer, a new batch of T-shirts thumbnails is loaded in the page content pushing the footer away…
Someone didn't think that one through.
Edit:
> Artists/Designers receive 1 Euro per shirt sold or USD or GBP equivalent. You also retain all rights to your artwork before, during and after it appears on Qwertee (most other t shirt design sites want ownership of your design forever).
Threadless legal notice states you own and will maintain ownership of your design(s) after submission.
I have a few, and am satisfied with the quality (but only satisfied, they're still a bit thin.)