You should have checked the position fully before agreeing to the stud wall.
However, the landlord cannot unreasonably with hold permission and none of the objections are reasonable.
An additional bedroom will add value and in any event you can remove it easily before handing the property back to the superior landlord. The fire brigade say that it is ok by them. The multiple occupancy argument is a joke, you could have 20 people in there with or without a wall and there is a separate remedy for that.
I would stand my ground and tell them that you believe consent is being unreasonably with held and they will have to enforce the terms of the lease if they want it removed. I would also offer to reinstate the flat to it's original condition after these tenants leave. The chances are by then everyone will have forgotten all about it.
I hope this helps.
If there are any further points please reply and I will be happy to respond.
The management company may have you and you neighbours as shareholders but the company is unlikely to be the superior landlords. Management companies are usually set up by landlords to manage the property.
For the letter follow the format above but put the points about the refusal being unreasonable in bullet form.
I would wait until after the letter has been sent to finish the work.