Thanks everyone. It seems that Rocket is the one, although Foremost sounds as good. Wish I had cherries, Hot Potato, I love them.
As for breaking up, I wondered about conditions too, Tim. I've always grown in soil before, but this time covered the seed potatoes with a thick layer of rough compost instead, so that may have made a difference. Next year will try some of the same variety in soil and some in compost and see if there's a difference.
Of course, if it's the weather conditions that affect growth then I'm done for - not a lot I can do about that. However, a few of last year's "escapees" have grown plants, and some of those dug up and cooked fell apart in the familiar fashion. Can't remember the variety, but it wasn't Rocket or Duke of York.
Interesting to discover that D of Y is an old variety and not early. It was definitely labelled "first early" on the pack.
Sue