They're after my wisteria!!!

[WhatTheWhat]

I have two questions for the legally knowledgeable out there - really grateful for replies!

Next door is a house in a poor state of repair that is let out to students. It has a large hedge adjoining our front garden. We have a large wisteria growing over our bay window, it's been there for at least 30 years and is right next to our property wall, but about 2m away from the boundary. The managing agents' surveyor has said that the terrible state of their property, including cracked stonework, is not due to lack of repair, but rather due to the hedge and possibly the wisteria.

(1) We like the hedge as it affords privacy and shields the view of their crumbling property. They now want to cut down the part of it that is closest to their wall. The hedge is about 30m long, L-shaped and about 10ft high, so taking out a slice right next to our front door will look dreadful. It's wholly growing on their side. Can we prevent its removal or insist on its replacement with something appropriate?

(2) Can we fight their proposal that we would need to cut down our wisteria as well?

Surely your stonework would be cracked if the hedge and wistaria were the real culprits??

If the hedge is growing within their boundary then they'd surely be entitled to cut it back.

Can you not put a hedge/fence/wall on your land but between you and this other house?

We will put in a fence if they cut it down or back, but we'd need to chop their hedge right back to the boundary in order to fence or trellis it, which will be a bit yuck and I don't fancy a 10ft high fence along the boundary line.
I am more concerned about our lovely wisteria, especially if the hedge goes - we're right in the middle of a city and greenery is valuable!
Mumsnut - we will certainly make that argument very forcefully if they do suggest we need to chop anything down on our side!

I think they would have to produce a surveyors report to prove the wysteria has such extensive roots to be causing this damage, they can't just SAY it is!