Am I doing it wrong? When laying up prepreg my gloves (from EC) stick so much to the carbon that I end up taking them off. It is particularly bad if heat is used when persuading the stuff into shape. 

No, fairly normal. Probably a bit too warm in your work environment, if you can regulate the temperature to about 20 degrees then that's typically when pre-pregs are at their optimum tack. From memory, the EC gloves are also quite thin. You can get thicker gloves that are more robust and make it a bit easier. 

Its otherwise just part of working with pre-preg, you get used to it. You can leave the blue backing film on as you get the ply mostly into place and then peel it off just before you press it firmly down. Just make sure not to get any film stuck between plies. I also like to keep a piece of scrunched up backing film and using that to press things into place.