2" may be more of a challenge. Lavers leeds may have some, but i suspect that most of their stuff is 1". They do have a strange attitude at times.
There is niche timber (or is it niche hardwood) down in pontefract. I have never used them, but they list some interesting stuff. I found them to be quite expensive, but I probably didnt really know what the stuff i enquired about was really worth.
Duffield list 2" on their stock list,
https://www.duffieldtimber.com/uploaded ... 524533.pdf and I have heard good things about them. They are up in Ripon.
I would be tempted to have a chat with british hardwoods, tell them what you want and I am sure they will pull you out the 2" boards when they come in. it may be the best bet if you are using it for stock rather than for a specific project. Either that, or find an alternative timber as a stock- Cherry would be an idea, and there are a few suppliers around for that- scrawton sawmills springs to mind!
For a large city such as Leeds, we struggle for good timber suppliers.