There is almost certainly no exact record of the boundary's location available anywhere. It's not just me saying that; it's what the Gov.uk site says too:
https://www.gov.uk/your-property-boundaries
This blog post from Adam Hookway (Customer Policy Manager at HM Land Registry) says much the same thing:
https://hmlandregistry.blog.gov.uk/2018/02/27/drawing-the-line-on-boundaries/
I certainly wouldn't assume that the boundary is formed by a line midway between AC and BD. The (1970s) house I live in is part of a square block of four. The block is square, each house within it is square and the whole arrangement is as geometrically logical as it's possible to be. It would therefore seem 'obvious' that the boundary between my property and a neighbouring one would be formed by a line starting from the point where our walls meet and running at 90 degrees to the common wall. However, until I sold part of my garden to the neighbour, the boundary actually ran at a 110 degree angle to my house's wall, apparently just because the builders decided that's where it should be!
If your neighbour owns the dividing bushes, he might actually have a valid case (although proving ownership of the hedge wouldn't, in itself, prove ownership of the land upon which they're growing).
You
might get some further information from examining the title plan of the neighbour's property (as well as your mother's one). It'll only cost you £3, so it could be worth a look:
https://eservices.landregistry.gov.uk/eservices/FindAProperty/view/QuickEnquiryInit.do
I'm sorry that this post doesn't really take you very far forward but, as I've indicated, there can be no definitive answer to your question.