Hi

I have seen this before and a friend of mine re plants them, not sure if this is much help not done it myself so good luck

I think I'd leave well alone at the moment Barry. We've had one heck of a cold winter, for the UK, and it's not over yet. Wait until spring / summer and see if your palms have survived. You may need those basal shoots to regrow your palms if they're dead. I certainly wouldn't cut them off yet, whether you want to try and use them as offsets (make sure they come out with as much root as possible) to make new small palms to plant somewhere else, or - if the palms you have are dead, you'll need to cut off the trunks and let the shoots grow in their place.

Agree with Beattie - probably your palms are Cordylines, and its entirely possible the tops have been severely damaged this winter - if the trunks or stems are soggy, you will need to cut back past that, or to where new growth is occurring, or you will have no cordylines at all. Leave those babies in place, do nothing till at least May, when you may need to cut them down to the base, or to where new growth occurs up the trunks.