Just an errant thought, but going through moneysupermarket and similar sites, there's tons of 'insurers' but a ton / most / all(?) seem to be underwritten by the same company, BISL. 

Why is this? And doesn't this create a problematic situation?

I'd be interested to read what you think the problem(s) might be ...

competition? or lack thereof?

Yup, this. (sorry for late response). If it's all BISL underneath, competition, quality of service etc would suffer?

Just starting to explore self build insurance.

My quote from Self Build Zone just now shows Markel International Insurance Company Ltd as the underwriter. It's the first of my researched portals.....