Right then:
I haven't looked for a new, new mobile yet

But, I have managed to get somewhere with the landline.
I rang Philips consumer helpline, who deserve a mention for being absolutely fantastic. Some of their models have a feature called 'do not disturb' and what that basically does,if I understand correctly, is still continues to have the handset ring when the incoming caller ID is known: but when it is not known, it stays silent which is much less intrusive and easy to ignore.
I have not yet managed to come across either a landline handset or device for the UK market (though there is one for the US) which does exactly what we were looking for - give a dead tone to everyone whose caller Id is not known. But this sounds like a good compromise.