I spent 25 years in sector ending my career as sales director of the largest manufacturer in the UK so I can probably answer this quite well.
99% of the production in the UK comes from 4 manufacturers Forterra, MBH, Ibstock and Wienerberger they sell direct to the major house builders and the rest is sold via factors and merchants. The pricing is done on a site address hence why they want a site address as if they register the project they get a higher discount.
With factories in Europe they all have distributors in the UK who they sell exclusively to, be it some of there range or all of it. These importers will also sell to factors and merchants.
Therefore the majority of bricks you get shown from merchants and factors will come from the same few suppliers. If you contact factories in Europe directly they will often just forward this on to their agents in the UK but at least you will speak to the importer directly. Depending on who they are they may sell direct or sell via a local merchant who they have a rebate agreement with.
When it comes to discount unless you are ordering 30000 bricks plus it’s unlikely to get a discount from the major factories as simply they don’t need too for smaller orders so any discount offered will be based on the merchant and factors rebate scheme with the manufacturer. Merchants will discount anything that they have on stock to simply shift it out the yard, especially in the current market however very few, if any, merchants will stock linear bricks