Phoenix Canariensis winter problem, USDA zone 8a?

I have a large 8ft tall Phoenix Canariensis palm in my friend's garden which was planted almost 6 years ago. When young, It was protected during the winter by tying up the fronds and covered in layers of fleece for the first 2 years then after that it had grown to about 5ft tall and was left unprotected for the next 4 years including this year. However last November we had a prolonged severe cold snap which lasted well over the christmas and new year period. I live in Britain, It is much milder now, although all the leaves have gone a very dark green colour almost dark brown and look battered due to high winds we recieved. Will the palm survive and outgrow this problem? thanks