Have you spoken to the council. They may have a view on this as it could be a hazard under the housing health and safety rating system.
Contact pest control / environmental health. The council may have a pest control service but will no doubt charge for any service provided.
It is not your responsibility to remedy unless the infestation is a direct consequence of any act negligence or default on your part.
Unless the council deem the property unfit for occupation your only option is to serve 2 months' notice to quit.
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