It's seems to me that the advice shelter give exacerbates the problem in the long term. Maybe not for the individual family that they are advising, but it becomes a vicious circle.
People rely on housing benefit because they can't pay rent on a place they need themselves, then when a landlord is completely reasonable in not wanting to continue a contract that has come to an end, the tenant can't find another private rental. But the reason they can't find another private rental is that they can't afford their rent, so they are high risk tenants. Then because they are high risk tenants for new LLs, they break the terms of their contract with their current landlord, and prove the point that they are high risk and LLs understandably want to take as few risks as possible.
There is so much hypocrisy shown on this thread.
People complain about professional landlords that control too much of the market by owning too many properties, but then complain that smaller LLs with one or two properties don't want to take unnecessary risks.
They complain that LLs don't stick to the terms of their contract by failing to deal with maintenance issues, then advise tenants to break the terms of their contract despite having somewhere else to go.
If the government wanted to help this problem, they could act as the guarantors for people who can't provide their own housing or pay their own rent so that they can access the private housing stock more easily. If councils would pay rent directly to landlords, but not hold them accountable if the claimant turns out to be ineligible then, and would pay for any damage the tenants might cause including overstaying their contract, then LLs wouldn't be so against taking HB tenants.