The landlord has no statutory obligation to repair outbuildings such as garages and sheds unless they are an integral part of the dwelling house.
The key piece of legislation that covers landlord repairing obligations is Section 11 of The Landlord and Tenant Act 1985 which covers the dwelling house (the structure and installations).
If the outbuilding was offered as part of the demised property it is reasonable that the landlord maintains it. If it was made clear in any marketing particulars and tenancy agreement that the outbuilding was excluded from the tenancy or that the tenant was responsible for maintaining it, it is not reasonable to expect the landlord to maintain it. Further, excluding the outbuilding from any inventory would make this clear from the outset as to what the landlords intentions were.
If the outbuilding was offered as part of the demised property it is unreasonable to expect the landlord to make repairs to defects that existed prior to the start of any tenancy and it should never be expected that the landlord should make improvements to the outbuilding – these would be entirely discretionary.
In all cases anything the landlord supplies must not present any health or safety risk to the tenant and should be maintained as such.