Essentially when you rent a place it's your home and you have an expectation of privacy and to not be hassled. AFAIK contracts are generally along the lines of 24 hours notice to come in unless there is a known emergency, things like neighbours smelling a gas leak. Once you're within either 1 or 2 months of the contract expiry date they should contact you to find out if you're planning to continue staying or even signing a new lease(as opposed to moving to month by month). Only when you signal your intention to leave is it deemed reasonable to show people around and while there will be times the place isn't available, you have to be reasonable in allowing this. But before you signal your intention to leave I don't think there is any legal basis or requirement to allow people to view, for selling may be different rules though as houses can be sold with the tenants and contracts in place.
Could you not just ask him if he intends to sell. He may have, like many landlords, a bunch of places and has no need or requirement to sell but his friends mum happens to be in a situation and he can help out a friend. So she may be the sole person he intends to show the place to, in which case I'd allow it. He may say he hadn't thought about selling but as his friend asked about the place for his mum he's realised now is a good time to sell, but at least you know one way or the other.
This is the first real place I've moved into that wasn't student accommodation, even then the first place was a refurb so no existing tennants when we viewed, the second place I knew the guys. The idea that for a couple months after I give notice here random people can and will be viewing my place is, creepy, irritating, I understand it but I wouldn't want it to be going on for months with no idea when they want me out at all.
Better to be open, honest, ask the guy and save the stress of wondering.