NO, its between the properties and shared, it's a PARTY WALL and you need
to
comply with the Party Wall Act - you'll need a legal agreement from your
neighbours to do anything that impinges on the wall or the attached
structure - please believe me, I have to get agreement from neighbours in
order to convert my loft, as despite the wall between properties being the
demarcation, it's a party wall because we both have it as our boundary.

Actually, the Party Wall Act means you don't need permission or agreement
from your neighbour. It gives you the entitlement to modify, strengthen
repair or use it. The main thing it gives your neighbour is the right to be
informed of the work and the right to appoint a surveyor at your expense to
ensure that the works are done safely and compensation for damage is paid.
They can't refuse you permission. If they try, the courts can (and will)
issue injunctions against them interfering with the work.

Christian.