See "rash guards". They're light-weight UV-opaque T-shirts that are intended to get wet, essentially. I wear one, and I do not burn under it, even at the beach, in the sun, all day. Do not forget to apply sunscreen to your hands, since it doesn't cover them — I made that mistake exactly once. (And other exposed areas, of course.)
Excellent quality, and their clothing really works. (I wore their Water Sports shirts extensively while swimming and diving in south Italy, where the sun is fierce.)
"UV shirt" would be a far more sensible name than "rash guard", I admit. That was just the name I learned for them when I first found out they existed. (Which was in Hawaii, under a brutally unforgiving sun.)