Sawed a great big gap in all the main-looking stems I could reach. Then leaned out of window (and even off roof, though only a pathetically tiny distance because I didn't dare stick more than about 10% of myself beyond the parapet and I kept my eyes shut the whole time in case the ground reached up and grabbed me) and ripped off all the bits I could reach from there too. Then asked (very helpful) roofers to rip off any bits they could reach as well, as they a) had longer arms and b) didn't seem to be subject to the ground-reaching-up-and-grabbing phenomenon. My theory is since it has triffid-like roots going into the brickwork it has to be reduced to below critical mass in order to have any lasting effect. Months later, it is mostly dead but there is a sneaky bit right at the top that I think is planning a comeback. Possibly a triffid in disguise.