My bro-in-law is not allowed into his flat because an internal (supporting) wall has fallen down. He can’t even get in to collect clothes/belongings. He’s bedding down with us at the moment and it looks like it won’t be a quick fix. Can he legally stop paying his rent until the flat is fixed? Private landlords, if that makes any difference.

Look at the tenancy agreement.
In mine, I would be in breach of contract as a landlord not to have a functioning, safe and liveable space. Therefore a tenant could refuse to pay under breach.

In addition, my landlords insurance pays for alternative accommodation for tenants and lost rent to me.
It would not cover personal possessions he could not recover – that is tenants liability.

Get to local housing officer / Shelter / CAB quickly, and a face to face meeting with landlord.

I think you may be right Matt, I asked about this with decorating my old flat, the agent said if I wanted them out for a week I would have to provide alternative accommodation at no extra cost to tenant. Which seems fair enough !!

Witholding rent never a good idea, the landlord will have way more cause to evict. But really, he needs to speak with his landlord ASAP and see what they are offering, and good luck !!