Thank you for the replies John, Paul S. and Paul R.
Paul R. - Wow - That idea is excellent and it's made an enormous difference to the sets I'm using. I've made up a few plug tops with some suitable 0.1uF caps between Live and Neutral and positioned them around the building - and it's almost completely cured the hum - at least reduced it to a level which I'm quite happy with.
I think I might make sure I build in mains filter caps to radios which don't have them from now on.
Brilliant. Thanks Paul.
Kind regards.
From Mike.