Can my neighbour build against my wall?

If the wall is on your land

A wall standing wholly on your land is yours, and your neighbour has no general right to cut into it or load it. If they build an extension right up against it, the part that ends up separating the two buildings becomes a party wall under the Act's definition, and later work to it follows the Act.

If the wall straddles the boundary

It is probably already a party wall or a party fence wall, and your neighbour has rights to raise, thicken, underpin or cut into it, with notice.

Flashings

A neighbour building against your wall may cut into it to insert a flashing or other weatherproofing, provided any damage is made good. That needs notice too.

Paying your share, and theirs

If your neighbour later makes use of a wall that you paid for alone under the Act, they should contribute a fair proportion of its cost, valued at the time they start using it.

What to do

Look at their drawings, check what touches your wall, and answer any notice within 14 days. If work affecting your wall has started without notice, see work started without notice.