I don't believe your AST agreement would be invalid, based on knowledge and a little bit of extra research.
It might help if you indicated what outcome you are hoping for from this debarcle, for which you would seem to be entirely the innocent party. I am aware of your previous post - this one:
http://www.theanswerbank.co.uk/Law/Question1479160.html
I ask this because, if you want out, surely it is a simple case of giving the necessary notice (probably two months), so I can't envisage what advantage it gives you, if your agreement could now be declared invalid.
Briefly setting out what's I think has happened here and my analysis of the situation:-
There's potentially a planning issue between the landlord and the local authority because of the holiday let issue. There are various leading test cases over this (because of potential change of use class) including Moore v. SSCLG [2012] EWCA Civ 1202. However if the landlord has been doing this for over ten years, none of this matters as the landlord will have automatically gained lawful entitlement to use for the property in the current manner (which is Use Class C3a).
There's the issue of the landlord not registering your deposit in one of the approved schemes. But I don't believe this voids your agreement.
There's the issue between you and the local authority over payment of council tax (which you have unwittingly paid over to the landlord).
What are the local authority saying about that last issue to you?