Oh, I think I have an insight.
I have a keyboard shortcut that replaces me. by mailto:me.myself@domain.com (not exactly that, but a parallel using my real email address). It now seems to me possible that in Safari, but not in other browsers, when 1PW enters my email address on the NHS site it somehow also triggers the keyboard shortcut and so produces things twice. But this is still odd, as this behaviour only occurs on very few sites, maybe on only the one site.
(Added later) I have now checked this and if I remove the keyboard shortcut, 1PW behaves as it should. So it seems there is something odd about the coding of the website, that manages both to enter the email address as 1PW should do and in addition expands the shortcut when using Safari