If the vermin infestation exists prior to the commencement of a furnished tenancy, the landlord is responsible for tackling it; this duty does not apply if the property was rented unfurnished.
Infestations which have been caused as a result of disrepair to a rented property (eg rodents are getting in through holes in the wall or floor) are the responsibility of the landlord to tackle. They are also responsible for remedial work if the infestation results in further disrepair (eg damage to electrical wire or skirting boards).
The tenancy agreement may also refer to responsibilities of tenants and landlords regarding pest infestations.