Not sure if this will fit your budget of 35pound transfer, but some years ago we stayed at the Pueblo Indalo Apartments in Mojacar and flew into Almeria. These were very family orientated, basic 3* SC accommodation, we went SC and ate out all the time but you could get H/B as well. I used a tour op, but imagine you could book them direct and use your cheap flights.
You could try googling them and see what you get, plus check HT for any reviews to see if they would suit you.
It was quite a long coach transfer, but I'm sure it would be quicker by cab.
They were right on the beach, although you had to cross the road. The beach was a bit gritty from what I remember (we are pool people!)
Happy holiday hunting.