Very tall potatoes, are they all plant and no actual potatoes?

Carry on but perhaps without any more additional topping up and I think you should be fine. It sounds as though you've been sold maincrop (like the ones grown in farmer's fields) but there's no reason to worry.
Don't give them fertiliser for flowering plants though because that's made to produce flowers. I'll ask DH what he used to use on his potatoes when we grew them, but it'd be mostly farmyard manure (nice and smelly) as he didn't like artificial fertilisers.
I do know some fertilisers grow roots and others grow flowers but other than that .............. sorry not much help.

Thanks anyway, we havent used any fertiliser on them , I’ve reached the top of the bins ( around 18 inches) so can’t put any more in, they are turning into a hedge!
I might have to go and have a peek.......

I wonder if you bought the same ones as me? There was a promotion of potatoes in bins regularly featured in the press, which I bought. It seemed that no sooner had I planted the seed potatoes than they started growing. They have now reached the top of the bins and look really healthy. I'm hoping that's a good sign. The last time I grew potatoes, they were got at by slugs. This time I put newspaper in the bottom, which is supposed to deter them.

Wait until they start to die down, before digging up. Plenty of time yet.

But you must water very well or you will get very small spuds.

Ours still have greenery on them and no flowers, DH put his hand down, felt them and dug up a few for supper.

Consulted DH the farmer at lunchtime and he says just water them till the tops turn brown, then they're ready, and it doesn't matter how tall they grow.
If you can't wait he reckons gently feeling down into the compost without disturbing the roots too much you should feel the little potatoes growing. And not to put any more soil on unless some are showing above the soil and turning green.
You may get some little potatoes on the foliage, like baby tomatoes (they are the same family) but not to eat these.
Personally I know nothing of potato growing but everyone seems to be of the opinion that you should be fine.
Enjoy!

We have some the same in bins in the poly tunnel. Keep them watered and when they are ready the tops will turn brown and die back. Ours are just going so we will harvest soon. Turn the whole tub out and hopefully lots of little or even big beauties to enjoy.

I think that we are going to have a rummage and see

Just had a quick rummage under 1 plant, bad news,1 very teeny tiny potato, smaller than a marble, maybe it’s too early? I’ll carry on looking after them but it looks like a big failure to me, still I will have the soil for next years raised beds.
And the radishes are growing a storm.
I hate radishes.

You have got maincrop potatoes the tubers might not start to get large until August or even September. Potatoes vary a lot in their habit some have lots of tops, some don’t, some have flowers, others none.

I would keep at it, too early by far, I would resist looking until they are starting to die back. Mine are also looking very healthy, but they have been planted in a high quality veg compost as it was all I could get. They have been spoilt!

Don't give up hope!
Although we used to grow potatoes , never came across this problem. Many other problems though. In open ground.
Are they looking for light?
Do you have a compost box/bin? I used to throw unused dried up potatoes into ours and they came back again later in the year, or the following year.

Sounds as though I need to be patient, maybe they are main crop then, I should have kept the bag. They are in full light we have several tubs dotted around the garden and they are all very tall. I will wait until either the tops die off or August whichever is sooner.
Thanks everyone

Good news then. Teeny tiny potatoes will grow, but potatoes do need feeding. I'm a bit bothered by lack of food, there would be some in the compost but it will have been used up by now.
We didn't use artificial fertilisers on the farm as I said, but organic FYM is a bit stinky to recommend in a domestic setting. One thing my MIL used to do was to collect sheep droppings (from a field) and put a few in the bottom of a watering can to use on her vegetables.
It doesn't smell very sweet (!) but it grows spuds.
Not recommended for lettuce etc .............. for obvious reasons.

Oh dear, I was hoping to do without feeding, but as you say maybe all of the nutrients have been used up. I’m going to keep watering them as usual and wait and see, worse case scenario is that the all go onto the compost heap.
I used chicken poop for the pot plants, oh dear the awful pong and the flies!
So def not using that for veg.
Sheep’s poo , hmmm, I could get my bucket and saunter down the road I suppose......

By the way, you said that "instead of rooting, they had little bunches of leaves" Potatoes do that - the first sprouting shoots appear well before any roots. It is usual to spread them out in a light dry place until the shoots are a couple of inches long before planting them. Good thing you didn't throw them away!

My daughters seed potatoes had proper roots on after chitting , ours were a different sort and just had the leaves. It remains to be seen whether I should have thrown them away.?

Mine had no roots when I planted them, just shoots. The shoots are now pretending to be a jungle, I can't see the roots but I assume they have developed well enough to feed all that foliage.

Resist the temptation to poke around too much until the tops die back. Give them food and water and sunshine and try to keep the slugs away. They will do the rest.

You can use tomato feed for potatoes too. It was on Beechgrove garden programme tonight to feed your potatoes.

Anyone can grow potatoes. Just stick ‘em in the ground and keep them well watered. Never fed a spud in me life.

My first earlies are just about ready I reckon. All this rain is ideal.