It could be a sight which was available to the trade rather than made and fit in house by the likes of Jeffery and Rigby.
One of my Frasers has the same type of sight, which I assumed was from a Jeffery, but now your Rigby and possibly another with such a sight makes me think it was a feature available on any British rifle originally fit with a peep sight.
Of course, the Jeffery Manlicher I got from Tinker has a Jeff patent peep but all of the express leaves fold flat. I guess that is a good option for a peep equipped rifle too.

My Jeffery 450/400

My Fraser 303