Neighbors shed overhanging into my property along with Rainwater from his roof.

Depending on the size of the structure, your local authority planning department might be useful if he doesn't respond nicely to your communication.

Yes the existing boundary wall must remain the boundary

It should be a parapet style eaves where the roof runs into the boundary wall, not past it. Water collected his side of the boundary not on your side.

You need to check if he built it without planning permission, it’s very likely but double check.

Then you need to approach him and point out the issue.

My guess is that he’ll claim the previous owner agreed to it. If so, he needs a written agreement which should be provided to you. If he has this, things just got a lot more complicated and your next call is to your solicitor.

But assuming he doesn’t have it, he’ll probably say “there’s not much I can do about it now” - do not engage in any compromise, it’s his problem to fix. He might offer to fit a gutter on your side, that will solve the water issue but not the overhang.

Assuming he doesn’t fix it, you’ll have to report him to the council. He’s broken the rules for planning exemptions so it’s an unauthorised structure. They should require him to fix it or remove it.

What rules for planning exemptions do you think it is breaking? It's possibly unauthorised, but I'm not sure how you can say based on info in OP.

True in theory but I don't see a planning department getting involved in that if exempt in all other aspects as it would come down to legally defining the boundary position.

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Not a planning matter. For the reasons above.

OP has assumed the rear wall is the precise boundary. It may well be, but the council won’t make enforcement actions based on assumptions.

Plus neighbours could agree to allowed an overhang. It’s a civil matter between them.