This particular palm is not entirely hardy outdoors in the UK. Assuming its not in a pot, then check whether the soil around it is dry, if it is, water it well by giving it a good few gallons, or leave the hose trickling at the base of the plant for half an hour.

What matters is the growing tip - check inside the middle of the plant to see if there's green inside the brownish damaged growths you've shown in your photo. The plant's not dead at the moment, its not looking bad considering its been out all winter and its early spring; if the growing tip is undamaged, it will put out more leaves. In the meantime, you can certainly trim off damaged parts of leaves.

I forgot to mention its name - its Phoenix canariensis...

Thank you Bamboo. I will check the inner part of the plant in the morning. It has been outside since before I moved to the house 2 years' ago and certainly looked healthier until now. I will also give it a good water. It doesn't get much sun at all where it is positioned. But we have had strong winds which might not have helped. To trim the damaged leaves, do I cut them down near the base, or just the brown tops?

At this stage, just remove the damaged parts and any leaves which are obviously dead - if it puts out more leaves this year, then remove whole leaves if you need to. Its probably worse this year because we had a lot more cold nights this last winter compared to the previous two.

Thanks. I have given it a good soaking but the bad news is that the inner parts are also brown and the whole plant looks sicker by the day!

Ah well, it will tell you over the next couple of weeks whether you need to just take it out because its a goner or not!

I'll keep you posted. Thanks for all your help.