The perimiter wall that surrounds a small house we look after has just been used as footings for a extention from the the neighbours.

The wall is say chest height to start and now has breeze blocks cemented on it to form a wall that supports a roof making a new house. Obviously no finishing involved just raw breeze blocks.

Any idea if this is legal at all ?

To determine upon whose property the wall rests, a survey is required. Once the survey is in hand, you will know if the wall is on your property or neighbors. I suspect it has been up long enough so records of who installed it are lost.

Perhaps questions to the neighbor might develop information as to the reason he feels the wall is his to build upon.

While there are set back requirements in most areas, they are uniformly ignored and many structures are built right on the property line regardless of where neighbors buildings are. It is not encroachment until you are able to show where the exact property line is. The a court has to decide if the encroachment is "de minimus" or minor or major and whether tearing down the encroachment is reasonable.

Does the rainwater runoff from their roof now run down your side of the wall? Or have they installed proper guttering along the roof?

Preempt it by using the wall as a support for your carport.