Walls that straddle the boundary
Where a party wall stands astride the boundary, the general position in English law is that it is divided down the middle. Each owner owns their half, and each half supports the other. You cannot simply knock down or weaken your half, because your neighbour depends on it.
Walls on one owner's land
A wall built entirely on one owner's land belongs to that owner. If buildings on both sides use it to separate them, the part between the buildings counts as a party wall for the Act's purposes, even though the ownership does not change.
What the Act adds
Whoever owns which part, the Act gives a building owner rights to carry out certain work to the whole wall, such as cutting into it, raising it or underpinning it, in return for notice, making good and compensation.
Repairs
Where a party wall is defective or neglected and has to be repaired, both owners can be asked to pay, split by how much each uses it and who caused the problem. Looking after your own face of the wall, such as plastering and decorating, is your affair.
Checking your deeds
Land Registry title plans show general boundaries, not precise lines, and rarely settle who owns a wall. Older deeds sometimes carry a "T" mark showing who is responsible for a boundary feature, but it is not conclusive.
Common questions
Can I knock down my half of the party wall?
Not without following the Act, and never in a way that removes support from your neighbour's half.
Who owns a brick garden wall on the boundary?
If it straddles the line, it is usually shared in the same way, and the Act treats it as a party fence wall.
Where this comes from in the Act
Links go to the official text of the Party Wall etc. Act 1996 on legislation.gov.uk.