We'll do you proud.....wait, maybe not.

[#1]

I'm now a prospective landlord and have a ADSL (and associated phone line) installed in the property for monitoring purposes such as temperature, leaks, fire, Carbon Monoxide. We'd already taken the decision not to give access to the phone/Broadband to the people renting the place from us. If they want a land line phone, fibre, or ADSL Broadband,  they'll just have to pay the cost of installation for a line of their own, but subject to our installation conditions/rules such as prior approval, the location of socket, use of DECT and not wired extensions as we want no damage to the decoration/structure of the building. The renters will be paying for the original line as the cost is built into the rental, but the last thing we'd want is them tinkering with the contracts we have with our suppliers.

[#2]

All very sensible and no doubt you'll have a modern, fair and logical agreement to cover all that. 
The OP's situation, though we haven't seen the actual clause, sounds like an "antique" agreement with an unfair and irrelevant clause in it. So very very different. 

[#3]

@AlaricAdair - it's absolutely none of my business, and a million miles away from Plusnet Feedback, but I can't help thinking that it would be useful if you were to take on the cost of installing the necessary wiring for a tenant's landline&broadband service.  If you are offering a six-month tenancy, then a tenant might find the installation costs uneconomic, and you might find that the property becomes less attractive.  Also, if you were covering the cost, then you will be able to claim total control over the positioning of the wiring and the socket.

[#4]

@KK thanks for the comment, I was just trying to represent the view of the Landlord (Sinister Black Coat and large black hat). Wondered if the OP had inadvertently triggered action for services outside of his contract  for Broadband and consequently terminated the Landlord's services too. I could visualise situations where losing the original number could cause financial loss to the Landlord for reprinting stationery, changing web sites etc.

[#5]

@AA - oops, I thought you were being serious...
However, this thread has possibly highlighted the fact that BroadBand is rapidly becoming an essential 'utility' in any household.  It needs to become uncomplicated.

[#6]

@AlaricAdair
I am sure I didn't trigger anything that could have terminated the landlord's services. In fact, I was the one insisting on keeping the number that the landlord gave me after I moved in.
I tried to get more info from BT and you already know what I had been told.
I don't know what happened, but if BT gave that number to someone else as PN claims, then I don't know how BT could claim I can take over the same number myself and right away.
Do they just switch back to the property, if so, then, what about the customer who has allegedly taken that number?
I don't know who has the correct info. All I know, is that in order to respect a contract (unfair clause or not), I went through quite  a lot of trouble, just to end up with a new number anyway (for which I shall hope I am not going to be charged extra by anyone).
Luckily, the landlord is ok with it (maybe they know something I cannot find out, or maybe, they just don't care), but one thing is certain, once I move out, i have to leave the new number to this property for future tenants (hoping no one, PN or BT, is going to give me grief for it).
Regarding your decision to have the tenants to install a new line, this decision might really make the property seriously less attractive.
One of the things I check even before I make any offer is whether some broadband connection (not sure how else to explain it) is already at the property without me having to install anything new (like cables for a new line), then I am free to chose the provider and that usually doesn't have anything to do with the contract the landlord might have already.
The previous tenant terminates their contract, or they move their contract to the new place, then the new tenant brings their broadband and phone contracts to the property.
So far I have always been able to keep the same number, even if the property has been empty for a while. This is the first time I had so much trouble. I hope it goes smoothly from here.
@AA you are right, broadband is an essential utility and it does need to be simplified. Switching, moving or starting from scratch, should not be so stressful.

[#7]

@chiso I'm not intending any criticism and I'm sure you didn't want any action that would have caused the loss of the number. I do share your view that switching should not be so stressful.  At the very least the phone number should never be cancelled by BT without the prior agreement of the person with whom the contract rests. At present it seems anyone who rings up and wants to migrate Broadband can trigger the number cancellation.