You say they've been given another year's tenancy but haven't signed anything. If they are assured shorthold tenants (which they almost certainly are) then the failure to sign anything very likely means they do not have a year's tenancy. The agreement will be a periodic one, running on from the end of the last fixed term tenancy. This means the landlord can get them out at any time by giving 2 months written notice expiring on a rent day.
So they need to be a bit careful if they don't want to have to move. However, the excuse for putting the rent up is pathetic & stupid. I think the situation is that if they are on a periodic tenancy it can be put up, but if they were on a fixed term tenancy it couldn't be put up until the fixed term ended. They should check by calling the Shelter helpline or going to local CAB.