Hmm, that shouldn't have happened, naughty tree surgeon! But yes, it should be fine, though it depends to some extent on whether you're in a very cold region of the UK or a warmer one. The only thing I suggest is, given the break looks like it might be rough with jagged edges, go out with a very sharp pruning saw and recut the top cleanly, at an angle, to allow rain to run off. If you don't have a sharp, clean pruning saw, I'd get the tree surgeon who caused the damage to come back and do it, if possible. You may need to remove a few leaves to do it. Losing the top in this way means that at least two branches will grow from where its been cut, and it may force new growth at the base - but wait and see what happens as the season progresses. You may need to remove shoots you don't want by the end of the season.

Hi bamboo, thank you for yor advice appreciated regarding my cordyaline I've done as you suggested, hope it recovers and that the weather is kind to us in Scotland this summer ☺

It's more that it's been 'pruned' too early - many people cut their Cordylines down, but its usually done late May or June, to give it the best chance of recovery. Hopefully, as yours seems to be in a reasonably sheltered position, it should be okay.