The short answer is yes, they can.
A tenant taking premises within a building already in need of significant repairs will often seek to cap his contribution to the service charge so as to exclude the cost of carrying out those repairs.
In the recent case of Princes House Limited -v- Distinctive Clubs Limited a tenant taking a lease of part of a building was successful in negotiating a service charge cap for the first five years of its term. The cap was sought so as to exclude paying towards the cost of major roof repairs already required before it took its lease.
In the lease, the landlord covenanted to use all reasonable endeavours to repair and replace the roof but had still failed to do so by the expiry of the five year period during which the cap applied.