Yesterday after the new fence went up and the greengage tree came down

Oh, this looks horried. Hope you can come up with a solution which will suit both you..and your neighbours, otherwise some planting planning is seriously called for.

I would be annoyed as well. Plant boston ivy. It is beautiful . That is what was planted by previous owners of this house on an ugly concrete retaining wall and it became a focal point. Especially this time of the year. It spread over to the house and we let it grow there as well.
You can see it in my gallery of pictures here on GOY.
Maybe you can ask your new neighbour to buy you a new tree. They should not cut the one on your property.
It is important to have a good tree to atract the birds.

It looks shady now but the sun is low. It is going to be much brighter in the summer.
Good luck and looking forward to see the pictures of your new plantings.
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Its bare at the moment but will change completely when you have planted something there,you have an opportunity to do many things there now....