Is this damp?

[KarbyBugger]

What's this on the brickwork at the base of our house?

Possibly, hard to tell as it's been painted over. But see how it stops at the mortar line? That's because that is where the damp proof course is, most likely. The bricks below the damp proof course will naturally be damp.

It's not above that line at all - is it maybe more that painting damp bricks is a mistake?

Moisture gets into the bricks below ground level. It then wicks up and gets stopped by the DPC. In this case, it’s also trapped by the painted brickwork. Eventually the water will force the paint off the face of the brickwork.
It’s best to never paint below the DPC, and even when painting above the brickwork, use a breathable paint.

How old is the property?

@TMMC1 it's from the 1930s.