You give a totally ridiculous example to justify your position. I very much doubt if you had a fire, your first point of call would be Wood Management either?
A blocked drain inside an apartment is one thing, the communal pipe is another. As a leaseholder I would expect Wood to see to the communal pipe, I would not expect them to attend to the plumbing in my flat unless further inspection identified a communal plumbing issue.
In the past I rented at Rainbow and my landlord was in the States. I had a plumbing issue that was attended to by a plumber, I then forwarded the invoice to the landlord.
I cant see where there is a problem here.