I think the problem is for other networks is their name isn't as well known as BT Openreach (as it was known).
On fibre lines only I would guess CityFibre is the next biggest. But their problem is the network branding seems to be hidden behind the serving ISP. I'm not sure how hidden. But I know many ISP's have multiple network providers and I'm not sure if the network name is shown within the marketing of their products.