Unfortunately, there is very little he can do.
I assume that it is a SVR mortgage and not a tracker. There are other considerations if there is a cheap tracker involved.
If her income is such that they will not give her a loan in her own name, there is probably no point in pushing her too hard.
If her income is good enough, then it's possible that she could switch to a different lender to get a lower rate of interest. This would depend on the current lender and the LTV.
He could go to the High Court to get an order to sell the house, but this would be prohibitively expensive. Of course, threatening it may well have the desired effect.
On the positive side, he has a stake in the house and as she is repaying the mortgage she is effectively building up equity for him.
If she were smart, she should try to sort this now as if she wants to sell at some time in the future, he can make life very difficult for her.
He should probably send a nice letter pointing out that it is in her interest to sort this out. He is willing to work with her to sort this out. If she refuses, then she will not find him willing to reciprocate if she ever wants to move house. He will also consider applying to the High Court to force the sale of the house.
Assuming she ignores him, then he should ask a solicitor to write to her, although it would be an empty threat.
Which bank is the mortgage with? It's unlikely that BoSI or Danske would allow him off the mortgage.