Is a lodger and occupier under the 1957 Act if they do not possess a front door key?

NO! All landlords in the US must give you 24 hrs notice ( some states even require 48 hrs) before entering any rented space. The only time they can go in with out 24 hrs notice is in case of emergency or to fulfill a repair request.

When you ask for something to be fixed you legally waive the 24 hrs notice. They are allowed to go in as soon as they can after the request. Once 24 hr notice has been given you do not have to agree to it or be there.

A phone message is legal in most states.

With 24 hours notice they can enter to do maintenance, repair or inspection.

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