If the trunks look healthy all the way down to the base, then leave them alone and wait till at least May or June to see where, and if, new growth appears. This might be up the trunk somewhere, or from the base. Once it does appear, cut down the trunk to wherever it is. If, on the other hand, the trunks have any soft, oozing or rotting areas currently, you will need to cut back beyond that point now, unfortunately.

I had an awful feeling it might result in them being chopped down to some level - I'll let you know how they progress. They're in a quite small garden so will be sadly missed - our neighbours always joke they wouldn't be surprised to see a monkey come swinging down!

Update on the cordylines - had both cut right down and we dug out as much of the roots as possible. We built a growing box over the remains of one and left the other alone. Last year we noticed shoots coming out of the 2nd and the new palm is now 5' high! The 1st one (under the box) also sent a green shoot out which appeared from underneath so we decided to re-site the box to give the shoot a chance - this palm is now approx. 4' high and both are doing really well. Patience is def. a virtue with gardening!

I wish a builder, all or any builders, would have read your post - they always think if they cut a plant right down, it won't grow back... and nine times out of then, that's completely and utterly wrong! Glad they recovered.

I've checked them today and realised that the 2nd one is actually growing into two separate palms so now we've got three! Because ours suffered so badly that particular winter (2011) we always notice other cordylines when we're out and about - even in the south-east they seemed to have suffered so we're really chuffed with the resurrection of ours.