Responsibility for local authorities comes under the remit of the Department of Housing, Planning and Local Government. However, the HSE also has a role under the Act insofar as it relates to rodent infestation.
Section 1 of the Rats and Mice (Destruction) Act 1919 states that any person who shall fail to take such steps as may from time to time be necessary and reasonably practicable for the destruction of rats and mice on or in any land of which he is the occupier, or for preventing such land from becoming infested with rats or mice, shall be liable on summary conviction to a fine.
I have been informed by the HSE that, if an authorised officer of the HSE is of the opinion that the occupier of any land has failed to take such steps as are required under the Act, a notice may be served on the occupier requiring him to take such steps as are prescribed in the notice within a time specified therein or enter upon the land and take such steps as are necessary and reasonably practicable for the purpose of destroying the rats and mice on the land or of preventing the land from becoming infested with rats and mice, and may recover any reasonable expenses so incurred from the occupier of the land summarily as a civil debt.