I'd say leave them and just allow them to die back. You don't say if they flowered. They will die away completely but spring back better than ever next year. My daughter is in Somerset and never covers hers.

Unless a very cold or cold and wet winter, you should get away without covering them. They will die right back to the ground in winter unless it is really mild, and the main problem is to prevent them rotting away with cold and wet.
When they come through in the spring, if you want large heads, do not let too many plants develop in the same spot, but reduce the number to two or three. Larger individual plants will produce bigger heads. Otherwise the artichoke will develop into a large clump with lots of small heads.
For the future, make a new plant in a different position every year by moving an offset in spring or late summer. That way you will always have new vigorous plants and can remove those that are flagging and getting old.

When we bought an old house with a very neglected walled garden, on clearing endless brambles there underneath was a row of globe artichokes, so they must be pretty tough.

Many thanks for the replies........i did'nt think cutting them back was right although up at allotment they have.....thank you again.

You will have to cut off the dead foliage eventually. If the allotment holders are doing it now it may be the best time for your area and will neaten your garden but I like things which are still standing up to remain over the winter as they do look pretty covered in frost. If you are always very busy in Spring do it now if you like. As Bertiefox says if the start to rot it can encourage diseases to get a hold.

Thanks again