Re: the legal position re: someone entering your home, I think the starting point is that there is something in law around "implied right of access" whereby someone entering the grounds of a property (normally opening a gate and walking down the path to the door) to make a delivery, eg parcel, letters, food delivery from Tesco etc, has the implied right to do that legitimate business. You don't need to enter into a specific contract with posties and Amazon/Yodel delivery drivers, that's why it's implied.
That right of access is implied until such time as the property owner wishes to withdraw the right of access, eg if someone repeatedly accesses the grounds even if for a benign reason, such as a JW wanting to talk to the property owner about their religion, then the owner can say to the JW that they withdraw their implied right of access (ie stop coming onto my property.)
Someone actually stepping inside the property takes the implied right of access to a whole new level, possibly trespass, although it could be argued that if the implied right of access hasn't been withdrawn, they were there on legitimate business and weren't a burglar - our village postie has been known to reach in and put our post onto the utility room counter top, if we leave our side door open in summer . We live in a rural community and we have a gate which we keep shut as it has an electronic alarm on so the minute someone opens it, we know they've entered the driveway and are walking up the path to deliver something.
There's city living and there's rural living, they are very different in terms of the trust people have towards each other. Posties have always had to take their chances with family pets, hence "Beware of the Dog" signs probably to cover the owner!