Thanks for your enquiry.
Your Brother's wife can ask that the house be sold at any time (as the property is in joint names). If your Brother does not consent, then his wife would have to take Court action.
The usual course of events is as follows:-
If either party were to issue divorce proceedings, an agreement over the division of all the financial assets, including the house, of the parties can and should be dealt with under such proceedings.
It would be normal for the parties to try and agree who should get what, and this agreement is then put in a Consent Order that the Court seals, and this then becomes a legally binding document. If the parties can't reach an amicable settlement, then the Court decides, looking at all the circumstances of the case.
Although I can't give any definitive answer as to how your Brother's financial assets would be split, on the assumption that there is equity in the property, the normal solution would be for the property to be transferred to your Brother, in return for him paying his wife £x amount.
No doubt your Brother's Solicitor can confirm the above and go into further detail when they meet, but I hope this gives you an overview.
If I have answered your question, I would be grateful if you could leave positive feedback.