They were issued in the War to keep heads warm under steel helmets. Up till then 'unofficial' headgear was worn.
They were very much an austerity design.
US Comforters were a lot better, they had a little 'peak' knitted on to the front.
Using a Wully-Pully sleeve isn't such a bad idea. If you get the right one they are Acrylic, not wool so you should have no problem.