That's a very traditional style. You see it around here, often mixed with flint, and with broken tiles built in as well. Some people erroneously call it a clunch wall (clunch is a weird stone.....more on that if you're really bored). This is a bit "samey" to match that vernacular, but nonetheless, apart from the ghastly mortar, that will make an attractive wall.
Chalk by another name! We've quite a bit of that round here - usually dressed rather than rough/random.
I hadn't realised that the term has been misused/expanded to describe not just the chalky stone material (whether dressed/shaped or not) to cover any wall made of inferior material - often in a rough/ragstone way, but not necessarily esp. "clunch-built" (which often as not, if Google is to be believed, has no clunch in it!).
Yes, chalk, but it's dug up from the ground wet, and doesn't dry into something hard for quite a while. This means it can be rough shaped with a spade/ adze/ axe/ froe, then set aside to harden. Around here it is sometimes used to build a whole building, and sometimes just used as quoins for a flint walled place.
If they were odd sized/shaped bricks it might look better. But the fact that they're regular sized/shaped bricks makes it just look messy. I'd also guess that this would actually take more effort and more forethought ... so no .. I don't see the point.