Pest Problem Arose, Landlord refusing to deal with it, is this clause valid?

‘The landlord will be responsible for any pest infestation up to 2 months into the beginning of the first contract if a single tenancy, or up to 2 months since the last tenant moved in on a HMO individual room let property. Subsequently, should pest infestation be discovered thereafter all liability would remain with the tenants to resolve. In addition at the end of tenancy should pest infestation be encountered, a full report shall be obtained by the relevant professional company outlining the same and all costs chargeable as the tenants’ liability until completely resolved.’

We have spotted a few cockroaches in our bathroom, the space is clean and tidy and we have taken steps such as repellent and commercially available cockroach killer.

There are a few holes which the landlord has said it is our responsibility to plug. We have lived in the property for 1 year and 3 months.

Is this the correct legal position?

Thank you in advance for your help.