Ok, many ideas given so far, and I've thought about the cost and
environmental aspect and decided not to go for an electric heater.

The pool cover I have is bright blue polythene and gets very hot in the
sun.

Would it be best to pull the cover taught over the pool so that it does
not touch the surface (i.e. a 6 inch gap between water and cover), or
let the cover sag so that it touches the water?

Or, is it better to let sunlight penetrate the water direct and remove
the cover during the sunshine?

I A-level physics, and we never covered swimming pool thermodynamics
;-) I got an E anyway, so even if we did I'd probably get it wrong !

Boz