Thoughts on cutting our trees

We’re moving into a home that has large trees in the garden, they don’t cause any shade to our garden but do block sunlight from the properties that back onto our garden.

For the past 30 years the cost of trimming the trees was divided between our house and the two properties who benefitted from the trees being regularly cut. Someone new has moved into one of the homes at the back of our garden and is insistent on us cutting the trees asap but refusing to contribute financially.

How would you handle this situation? We will want to cut the trees at some point so they don’t get too large but it feels a little unfair to be pressured into doing it at a time that suits them.