Could it be frost damage?

I'd get them inside, dry them off a bit and keep everything crossed.

I would dismantle the basket and start again.......

I agree with AmbleA dismantle and start again.

Have you got a greenhouse? Then if so put them in there and as seab says fingers crossed, dont give up on them, this is going to be a tough summer. Maybe at least give them a couple more weeks.

Hanging baskets should have a way of getting rid of excess water. What type are you using eg wicker baskets, solid plastic bowls, wire mesh with a liner? The problem can recur if you do not find out why it happened.

Exactly my thought, Scotsgran, I'm finding it hard to work out how you could possibly overwater a basket or a pot - they should all have drainage holes to let excess water out. Unless you've one of those plastic hanging "baskets" with a tray underneath, then it might get waterlogged, I guess. Doesn't explain why the pots are waterlogged though - make sure you've got good drainage, and keep them inside at nights particularly until all risk of frost is past (end of May) - that's what's caught the tops and made them black.

Well done the experts, getting to the root of the problem!