It can often be a bit of a 'catch 22'
But just as a first step, had you considered a new joint bank account at your existing bank.
Take the option to have paper statements sent every quarter.
Also how about your water supplier.
Once she has proof of address there are probably a few other sources she could tap into.
Usually when registered at the GP she will receive an NHS medical card.
Also don't forget application for National Insurance.
Writing for confirmation of something from Inland Revenue or indeed the Home Office can also result in acceptable documentation.
Time for thinking caps I guess.... Good luck.