I really don't understand how an "external brick wall" can also be at the same time a "fire-wall at roof level".
A "fire-wall at roof level" sounds very much like an internal wall in the loft space, not an external wall.
Is this some vertical wall that goes up the front of your houses? I'm very confused indeed. I know that this is a real MN cliche but I really do think that we need a diagram here as I jut can't envisage what this looks like at all.
But, if this is something that is on the boundary line between the two houses and it is necessary to make good or repair the wall "on account of defect or want of repair of the structure or wall" (Party Wall Act, Section 2(2)(b) ) then it does come under the Party Wall Act.
If one party serves a Notice on the other party then the cost will be split depending on who caused the lack of repair and/or who uses the wall the most. In this situation it would likely be a 50/50 split as neither of you likely caused the damage and you use the wall equally.
This is specifically referenced in the Act (Section 11(5) ). It says:
(5) Where work is carried out in exercise of the right mentioned in section 2(2)(b) the expenses shall be defrayed by the building owner and the adjoining owner in such proportion as has regard to—
(a) the use which the owners respectively make or may make of the structure or wall concerned; and
(b) responsibility for the defect or want of repair concerned, if more than one owner makes use of the structure or wall concerned.
I would strongly suggest that you speak to a solicitor first (see if you have legal representation available under your home insurance for example).
From there you would likely have to give notice under the Party Wall Act that repairs will be done to the wall and that they are required to pay whatever percentage of the costs is appropriate.
Either that or, if you think that they won't pay, and you don't want to cause a dispute then just suck it up and either pay it all yourself or wait until it collapses.
Anyway, you may also want to speak to your home insurance company as they may well foot half of the bill anyway and look to your neighbour's insurer to cover the other 50% of the bill.