Single brick wall and building regulations

FreeBear

A standard brick is approximately 100mm wide - Older bricks could be anywhere between 95mm and 110mm depending on the age and region.
A wall thickness of 150mm would be made up of (very roughly) 25mm of external render, 100mm of brick, and 25mm of internal plaster. Or if no render externally, 100mm of brick, 25mm battens, and 25mm of lath & plaster.

Dedekind

So quick update: the builders who said it would be doable actually misunderstood our request. They are coming back to discuss more options and take a closer look.

In the meantime we managed to talk to one of the council surveyors. They have no issue being single brick, and what they suggest is have a builder dig up along the wall to check the foundations. Then call a structural engineer (which needs to come anyway for an RSJ) and ask him what he thinks. If he thinks they are enough to build up on top then the council is fine with that.

Now, he did suggest it's an old structure, the roof will not be perfect even if rebuilt and if we are spending money on it then we might just as well rebuild since otherwise it will not look as good and will have issues (roof not straight, bumps, things needing fixing often, etc).

So we are almost definitely learning towards rebuilding.. at the expense of leaving the living rooms/hallway refurbishment for the future and just do kitchen and extension now.