How to clean 'rust?' from stainless steel radiator?

Looks more like chrome plate steel, in which case the rust is due to the chrome plate failing.

Umm...

I don't think that it's stainless steel.

Do the spots appear in the same places and is there pitting?

The radiator appears to be a plated one and so your options are limited to painting it, getting it replated or replacing it.

move it away from the toilet as urine is great for rusting most metals

Thanks very much for the fast responses and advice. I'm sure it must be the chrome plated type as advised.

I've just tried rubbing a wet cloth across it, and it comes up very well, so my description of rust spots was misleading. I'm going to see how well it comes up by cleaning normally.

I suppose that another thing that you could try is to use some kind of rust inhibitor liquid - clear one - carefully dabbed into the pits and wiped carefully. This may at least hold the rust back from developing to some degree but won't hide the marks.

you can clean rust off chrome pretty well as the rust spreads from teeny holes that don't show..until the pitting under the plating causes massive chunks to fall off.

Could try Autosol for cleaning car chrome ???