Thanks for all helpful comments and advice here, Waxon, Curious, Malmi, Fairy and others. Mumsnet is better than googling! You've not just reassured DS and me, you've shown her what to do for the best. (I would never have called police on her, but she was getting in a state about it so I was too.)
Even when the information you find from Google is correct, it doesn't always tell you what you want to know.
Google told me "Photo-card driving licences are set to become mandatory in 2015" but I should have continued to read "when new paper licences are officially phased out". I can now see that didn't include old paper licences, so pre-1998 licences are OK. I was panicking by then, which never helps.
I couldn't find anything, by googling or on government sites, that made it clear that, though having the wrong address on a licence can land you a £1000 fine, it doesn't invalidate your insurance. So thanks Dreaming of MrsG for posting a screenshot.
Invalid insurance was the most worrying, not just because it's illegal, but it causes major problems for other people if you have an accident. DS isn't the sort of person who doesn't give a damn. That's why she was getting so upset about it. At least now the most she has to fear is a fine. But I will try to persuade her to put in a change of address application.
Off now to give her the good news, so goodbye, and thanks again all friendly posters.