Great suggestions guys, and thanks a lot.
I took the plunge and pulled the fuel tanks out, and found a tiny split in one of the lines where it slides onto the aluminium tube through the bung, so it was sucking air. When I put my finger over the carb and pulled the prop through, it sucked fuel, but when the demand was increased by the running engine, air got into the line. All solved.
Thanks again for your help.