Spreadshirt? I've used it quite a lot and found it to be good quality, haven't ordered for about 18 months from them. I've got decade old stuff from them that's still good.

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).