Unless rents are going up (and in London they are not) I don't see how longer tenancies help you. It certainly doesn't give the landlord an incentive to fix.
Periodic (rolling) tenancies can be ended with two-month's notice, so the landlord might decide to evict rather than repair. With longer tenancy agreements, the landlord can't evict until the tenancy expires, and so tenants can use their legal rights to compel the landlord to make repairs.
In short, the landlord can't kick people out as an alternative to spending money on repairs.
Yes, they're technically "obligated" but only real recourse is to pay somebody to fix it yourself and deduct that from the rent. While doing that you have to be 100% reasonable though (no overcharging, get multiple quotes and landlord must be kept informed).
If you stop paying rent because repairs aren't made you can be evicted.
And then you get evicted after the negotiated period ends anyway.