Which fence is yours? Boundary ownership explained
There is no left-hand-side rule. There never was. Here is where ownership is actually recorded.
The rule that does not exist
Almost everyone has heard that you own the fence on one particular side of your property. It is not true, there is no such rule in law, and people who repeat it disagree about which side it is, which is a clue in itself.
Where it is actually recorded
Boundary responsibility is shown on the title plan registered with HM Land Registry. A T mark drawn on one side of a boundary line indicates which property is responsible for maintaining it. An H mark, effectively two T marks meeting, indicates a shared responsibility. You can download your title plan for a small fee, and it is worth doing before spending money.
Many titles carry no marks at all. In that case there may be nothing recorded, and responsibility falls to what the deeds say, what has been done historically, or agreement between neighbours.
Why it matters practically
Paying to replace a fence that is not yours does not make it yours. It also does not create an obligation on your neighbour to contribute. Separately, taking the opportunity to move the line even slightly while a fence is down is one of the most reliable ways to start a boundary dispute, and those are expensive out of all proportion to the fence.
The practical approach
Check the title plan. Speak to the neighbour before work starts, particularly about access, because replacing a fence usually needs both sides. Agree in writing who is paying for what. Photograph the existing line before anything comes out.
If you want this looked at properly, Shrivenham Fencing covers Shrivenham, Faringdon, Highworth.