The gadget you need is a line stripper. ABU and Berkley make one and it comes with a reel spooling station. The line stripper is powered by a couple of batteries and you place the loose end of the line between two wheels and start it up. It then strips all the line from your reel. I got mine from Alderney Angling, great service and well packaged www.alderneyangling.com/tacklebaitprices.htm
They do it for £20.99 with free P & P. You may be lucky and find one on E bay.
You can buy the line stripper separately for about £10 from most tackle shops but the Reel Spooling station is well worth having. It's not something thing that you would take out with you but when you are at home and want to change your line it is there.