Even though spain is catching up fast with the modern world, its still mainly a facade. The attitudes and institutions are still decades behind the uk.
I work in webdesign/IT so maybe i am biased. But its still worth hearing: most of the property we have rented (over years) has come from word-of-mouth. We ask everybody we can, friends, estate agents, local shops, etc... and after four to six months the offers start coming in thick and fast. The verbal route is still the primary method of doing business.
And remember, if you sign a 12month contract, the landlord is legally restricted of putting up the rent (for something like 5 years!) - so expect 11month contracts, or odd ones not worth the paper their are written on.
Carry your passport with your driving license. If anyone askes show the two. Dont show your id/residence card if you have one.
Its worked for me, for years (and i have the old type of license thats valid for 50 years or something daft).