I'm going to investigate all the recommendations in this thread.
So far, all the accommodation we have secured for our Spain trip has been through AirBnB, as we really like to have the flexibility of making our own tea/coffee and snacks as we go along, as opposed to having to rely on restaurants for everything. We probably won't do any serious cooking, even if the equipment is available, but it's nice to have the option if we decide to do that.
I've found that many of the apartments advertised on AirBnB and VRBO in Madrid do not meet our requirements. i.e Elevator, walk-in-shower, 1.50m (Queen size bed), but nonetheless, I'm pushing on.We might have to stay in a hotel if I can't find an apartment.
Just this one last piece of the jigsaw to put in place.