It is essentially a negotiation. There is plenty of scope for a resolution as they want to stay and the landlord wants them to stay.
London prof tenants would be demanding alternative accommodation by now. And if he had full landlord insurance (many dont, including me) its the sort of thing insurance would pay for.
So no rent during building work is relatively cheap.
Are any of the parents surveyors or solicitors. I think this is one of the instances where a parent might step in, and talk to the landlord, with the locus of being a guarantor. Alternatively if it is a registered HMO they could talk, or threaten to talk to, the Council HMO officer as parts of the property are clearly not fit for habitation. DDs last year landlord used a management company. The junior staff were young and inexperienced, but the manager was an old property hand and stepped in at one point to remind the landlord of his obligations.
The fact that the landlord is offering 20-30% suggests he accepts he should pay something. All landlords are tight (including me, you dont make money unless you watch the pennies) and I would expect that if he met resistance he would go higher. He needs to get the work done to protect his property, so needs their cooperation.
If they can be assertive whilst maintaining good relations it will be a positive life lesson. But basically why it will be a lot easier for someone used to negotiation to take it on.