I don't know why you're overcomplicating it - just don't allow viewings. Few people will want to buy anything without at least having a quick look inside.
If you've got an AST, you have a right to peaceful enjoyment of the property - the landlord does not have any right to enter, or to give keys to an estate agent, regardless of what notice they give.
You may not own it, but it is your home and you do have the right to control who comes and goes during your tenancy. Of course, if you get on with your landlord and don't mind people traipsing through your house at all times of the evening and weekend, ignore the above. But then you probably wouldn't be asking the internet on how to put them off.
Just politely, firmly, refuse to allow viewings until your tenancy agreement is finished.