Oh dear, another casualty of our bad winter. Leave it until at least June before chucking it out. Then but Trachecarpus fortunei as it is the only reliably hardy palm in the UK.

Chamaerops humilis is one of the few palms that can sprout at the base if the main crown is damaged. I'd leave it until July or August, in case it decides to do that, since it needs a lot of warm weather to encourage it. In the meantime, cut off any yellow or brown leaves, and be prepared to cut out dead trunks in the summer.