Potatoes are pretty tough - after all, the volunteers come up ok!
I planted mine (all second earlies) out at the end of March and, as it was nice weather when they came through, did not put fleece on them. Cue a frost (and we have not had many this winter). The tops were browned but they will grow back, so I put fleece over (stable door horse after bolted locked). A couple of weeks later, I am going on holiday, the weather looks mild and damp, so I take off the fleece, water them well, and earth them up. I returned this weekend, everything looks dry despite some rain, and the potatoes have been frosted again, but are already bouncing back.
So don't give up on them.