Neil,
At Alicante, you have Airoway. They rent planes,are cheap, but be aware that training is only done in Spanish.
Further North, in Valencia, is of course Airmed. Everything is done in English there.
Spain is a full JAA member, and all hours are recognised by the CAA.
Be aware that Bae Jerez is now also a Spanish school, issuing Spanish licences and not British ones.
Murcia/San Javier has no flying schools/clubs in my knowledge.
