If a tenant takes steps to mitigate an infestation problem, they could argue that responsibility for pest control shifts back to the landlord. For example, if the tenants cleared rubbish that was attracting mice and the infestation remained, pest control could then become the landlord’s responsibility.
That said, this isn’t always clear-cut. If an environmental health officer concluded that the infestation was due to a tenant’s negligent behaviour, the landlord would have a strong case to argue that pest control remains the tenant’s responsibility.