The only thing that I would add to Lawcruncher's excellent summary is
1: Refer to the tenancy clause allowing access, and state the purpose clearly.
2: If you intend to use landlords keys, say so.
3: Be sure that the notice you send is going to be received in good time and don't rely on one single method where more are available. Unless its an emergency most inspections/ gas checks etc can be planned & notified well in advance.
And a good investment in any home is a simple safe to put their mind at rest over valuables going missing.
Based on the information posted, I offer my thoughts.Any action you then take is your liability. While commending individual effort, there is no substitute for a thorough review of documents and facts by paid for professional advisers.