As the title asks. It's such intense legalese that I can't get my head around it!
Short answer Maybe
Long answer s.61(1) empowers a "proper officer" to enter premises without a warrant for the health protection functions and purposes described in subsections a-to-d in order to search, take samples and measurements, inspect records and any other actions authorised by s.62(1A).
A Proper officer is not a constable, but defined at s.74(b) as being a person appointed for a particular purpose (ie function or role) by the relevant authority.
s.62(1) allows the proper officer to take with him anyone necessary, which can include a constable who may be required to facilitate a forced entry, prevent a breach of the peace, make a pre-planned arrest or perform any number of police-specific functions.
However... s.61(2A) states that this power of entry does not extend to a private dwelling; which may or may not be the house referred to by the OP. Entry in to a private dwelling requires a warrant under s.61(3).
If they are “authorised officers”, yes
The relevant provisions are in section 13.
Subsection 4 gives the minister the power to make regulations to nominate certain bodies to enforce the law. They may authorise people (who may be police but could be others) to be “authorised officers”.
Subsection 5 gives those authorised officers the power to enter premises “for the purpose of executing, or superintending the execution of, regulations under this section.“