Hi, I have the number of an English couple who rent out rooms in there house kind of like a B&B without the second "B," just the bed. They are charging my Mother and Father- in-law 50 euros for 2 night in June for the pair of them. The only downfall is that it is near the Benidorm Palace so isn't exactly central. If you are interested then you could P.M. me for there number.

Sue

Try Benidorm reservation centre (Beninter).

http://www.beninter.es/indexengjs.htm

Apartment blocks Gemelos 2 or 4 are very central, so is Gemelos 20 but it's dearer and not really worth the extra, just a newer building. Horreo is also central but the pool is a bit crappy. There are other blocks but I haven't stayed in them. They also handle hotel bookings.
There is another agency called Gestaltur who handle mainly the same apartments and hotels, but they only do Saturday changeovers. The advantage of both of these agencies over some other websites is that they have their offices in the town (both very close to the apartments I listed) and English speaking staff, so any problems (extra keys etc) can be handled easily.