Thanks for all the suggestions, and sorry for not replying bit sooner. Back from holiday now.
Seems I didn't make my quest clear enough. When I said 'longest climb' I think I really meant 'highest continuous climb'. The various Mt Tiede climbs in Tenerife apparently have that record for 'Europe' since they rise from almost 0 to 2200m, over 30 km, without any noticeable descents. But as I said I don't really qualify Tenerife as being in Europe.
A very long climb at very low gradient (e.g. MickF's 20 mile A9 climb) doesn't win because it only goes from 200 to 450m (hardly a climb at all really
Some of you mention climbs in Spain, Italy and France which seem to go up more than 2200m. The Pico de Valeta climb in the Sierra Nevada looks a contender: according to RideWithGPS, from Granada it up goes from 700 to 2500, so a continuous climb of 1800m. I don't think I'd allow unsurfaced roads so the climb up the other side from Orgiva doesn't qualify!
I'll try mapping some of the other French & Italian ones mentioned - or be happy to see the results of others' work in this respect. When I find the 'winner' I'll make it my next challenge. Europe only please!