An update on this one. Went to Kwik-Fit this afternoon, asked them to do the valve, do the tyre pressures on the other three, give me four plastic caps to replace the idiot metal ones with the fancy BMW logo on them, stick a litre of oil in and give the brakes a once-over while they were fiddling around with the wheels.
Cost: £0. Litre of oil top-up was free for customers doing other things. Once over is always free. Valve was simply wheel off, depressurise, replace valve, repressure and refit so they felt it a bit much to charge for it. Still, 20-ish minutes of their time and their equipment, plus the oil, valve and caps. They were insistent there was no charge.
I donated £10 to their tea-fund and fully intend to go back there when I need new tyres.
It's nice getting service where you walk away happy on all fronts.