a steely determination not to take any nonsense from anyone

Yay! :-)

not even nice cheese – perhaps that plastic cheese-alike you melt on top of beefburgers

I tend to buck the trend and use nice mature cheddar personally..

I find mature cheddar doesn't taste quite right on burgers if it fails to melt properly; I suspect plastic-imitation-cheese is specifically designed to have a low melting point for this purpose.

That said, I found some thinly sliced Port Salut in Sainsburys once which seemed to work rather well; I don't think it melted properly either, but it didn't seem to matter so much.

From what I recall, the blue cheese that Red Robin (http://www.redrobin.com/) used one burger was perfectly adequately melted - it wasn't quite as goopy as processed cheese is expected/required to be, and was quite nice.

Red Robin: thanks! I must try them out. It transpires that there's a couple near us.