An update, just in case anyone else has this issue - I spoke to B&O about this; in summary they said that the platters originally had a clear-coat sprayed on them, and that this had probably been damaged and that the only way to fix it would be to get the platter re-coated, but that's not a service they offered, and they don't stock spares (no surprise there). So I decided to experiment!
I suspected that the clear coat had actually worn off some time ago (the platter is 30-odd years old and any coating is unlikely to have survived that long), and that the white was actually light corrosion of the Aluminium as a result of the loss of the clear-coat protection; so I thought i'd approach the restoration with that in mind.
Rather than use Brasso (as suggested by another forum member) I opted for something a bit less harsh - A mild silver polish I have previously used to good effect on cutlery (The can said it also worked on aluminium). Wow - What a difference! Starting gently at first, and interspersing with cleaning in cold Soapy water (and drying thoroughly), the marks gradually faded to the point where I have a platter that looks pretty good. The black markings on the platter also seem to be unaffected by the cleaning.
I'm sure further cleaning would improve the result even more (there are a couple of areas that still aren't 100%), but i'm not going to push my luck and risk ruining it.
I anticipate that the platter will degrade again over time, without it's protective coating (i'm tempted to seal it, but not sure what with, as I don't want to use something that will end up damaging the vinyl); hopefully it will do so gradually and more evenly than it did last time (which I suspect was as a result of a previous owner leaving the platter wet). In any event I'd be more than happy to repeat this process, given the result.