I've seen worse on older Westerlys, try oxalic acid on the rust spots, Milton soak on the bowl, and scrub with Cif. Might save you a fair bit. You could paint with two-pack, but not cheap and not easy to get a perfect finish. Flowcoat difficult as it doesn't behave quite like paint.
A stainless steel sink would be the most satisfactory but the difficulty will be finding a suitable sink the right size and fitting in to the existing galleyThis is the old sink in the longbow, can it be painted with gelcoat or something? or is the best option to cut out a rectangle and drop in a new stainless sink?