Thanks for the suggestions chaps!
I've tried most of them (but not vaseline....
Usually I eventually manage to extract the string, but it can take quite a while fiddling about...
Amazes me that these days when there are so many innovative upgrades and gadgets available to improve or correct such faults or issues with guitars- especially 'classic' models like Les Pauls, Strats etc, something as basic and obvious as assisting changing strings is overlooked..probably because such problems are not as 'sexy' and fascinating as pickups, vibrato units etc..I would think that a simple redesign of the string cavity holes in the vibrato block could work..
...which is why I always have a spare guitar close by when playing gigs...long ago I gave up on that business of keeping playing on five strings until the set break then faffing about changing broken strings in the limited time between sets etc..usually in the dark, backstage etc..