Former tenant threatening legal action

I would agree that the "substantial" should be something that improves or enhances the property like your suggestions and cannot be something that is cosmetic like painting or fixing things that are broken
But I think 3 months is to short to be considered reasonable when selling a property, in this case a minimum of 6 months imo would seem a resonable especially as their selling it themselves
 
The legislation allows for the termination of a Part IV tenancy where a landlord intends, within a period of three months after the termination date, to enter into an enforceable agreement to transfer to another, for full consideration, the whole of his/her interest in the dwelling or the property containing the dwelling.

The only issue of relevance here is whether a landlord genuinely intended to sell the property within three months at the time that he swore a statutory declaration to that effect. Unless a tenant can prove otherwise (and the burden of proof is on the tenant) then the termination notice will be valid (subject to giving the appropriate notice period).

Quite separately, the RPZ cap does not apply if, in the period since the rent last set under a tenancy for the dwelling:
  1. A substantial change in the nature of the accommodation provided under the tenancy occurs; and
  2. The rent under the tenancy, were it to be set immediately after that change, would, by virtue of that change, be different to what the market rent for the tenancy at the time the rent was last set under a tenancy for the dwelling.
That has nothing to do with the "substantial refurbishment" ground for terminating a Part IV tenancy.
 

I would tend to agree with Cervelo that six months would be a reasonable period.
Firstly, a vendor has to advertise the property and may well not get a 'viable' offer for several months. Then once the offer has been accepted, there could be a further 3 months before contracts are signed. So the overall time period would be close to 5 months.

Furthermore, a landlord serving a notice of termination where he requires the property for his own use would be in breach of said notice if he re-lets the property within 6 months from the expiry of the notice.
 
Again, the only issue that is relevant to the validity of the termination notice in this case is whether or not the OP genuinely intended to sell the property within three months at the time that he swore a statutory declaration to that effect.

That's it.

The OP has not terminated the tenancy for his own use so that is completely irrelevant to this issue.
 
OP having read through all the replies to your post, if I were you I would focus on the replies from Sarenco which are relevant to your particular scenario and seem to me to be on the ball. There are a lot of irrelevant posts on here which serve only to confuse matters.