Responsibility for overgrown tree that borders two properties

A neighbour has a large tree right in the middle of the boundary of her property and an adjoining property. This large tree is right on the end of her back garden, and also right at the end of the back garden of the opposite property. When the neighbour's property was built, they only got a wall for half of the end boundary of the garden, with a fence for the other half, because of this tree.

Given the wet summer, there has been considerable growth in the tree, and it is now very tall (maybe 1.5 or 2 times the height of the house), and blocking lots of light and dropping lots of leaves. My neighbour wants to arrange to get the tree cut back in size and well pruned.

She intends to contact a tree surgeon and approach the neighbour about sharing the cost, but was just wondering about the legal responsibilities in such cases. Is it significant that the tree was in place long before the neighbour's house was built?

She should approach the neighbour first before contacting a tree surgeon.
Simply to avoid any problems that may arise..neighbour may take offence if other neighbour assumes ownership of the tree.
It shouldn't matter if the tree was there before neighbour house was built..if it's partially on their land..they should have a say in it.

Suppose your neighbour can't afford to go halves on the price of getting a tree surgeon? Cutting just the branches that reach out over the wall won't solve the problem. You've no right to light but perhaps the tree is providing you with extra privacy? As tree grows it will become more expensive to remove. If tree falls it could damage your property or boundary wall so lots of considerations for a chat.

The tree may be causing more problems than just being overgrown. Our county council have admitted to us that they planted the incorrect trees near to our house. I'm convinced to this day that the problems that we had with cracks in our driveway and back wall were partly caused by the roots of these same trees.

Thanks for the comments. Any idea what would happen if one of the parties refuses to cover their half of the costs of maintenance? Can they be forced to share the cost by the other party (as happens in the case of shared drains)?

Complainer if the neighbour wouldn't pay I'd (a) leave things as they are and come back to it at a later date (especially during a storm!) or (b) just offer to pay his/her half and be done with it.