[mumofstig]

but the stem didn't look black in your photo  ...nothing at all like this 

[potatogrower]

best to break off the damaged leaves in case they let in diseases.

had frost damage on mine and broke the leaves off to be safe

[DD.]

In my opinion, you're best leaving frost damage as is, rather than breaking leaves off & leaving an open wound.

[Iain@JBA]

I tried to grow potatoes once in well rotted manure. It was a disaster. The manure looked fine when I first put it in containers but the manure then set solid during spells of heat and the potatoes could no longer get any moisture or feeding from the manure.

Any way my first thought was water scorch but then Saw that you hadn't watered which is why I wrote about my manure disaster above.

Another thing it could be is magnesium shortage? It does not look quite right for that either though.

I will have think tonight for what else it may be.

[Paul Plots]

Woodhousemoor - DD is most probably right = "frost" so you won't need to do anything just leave the plants to grow on... unless there's another frost in which case get them covered PDQ. 

[NASH]

I have pulled up a couple of wilted plants  now and they are very shrivled and black and snap from the seed potato, I just hope it does not spread too far !