Top tip if you can get to an agricultural merchant to get milkstone remover... very potent and much cheaper than using proprietary stuff. But to be handled with extreme care: it's pure acid.
Thanks - was totally unaware of that! As it happens I already have a bottle of high-concentration (I forget what) phosphoric acid for rust removal, although I don't fancy chucking any down the bowl. I'll see how the vinegar does first..