British hardwoods is worth a visit (not sure how open they are at the moment). The website won't show you what they have.
But they probably don't have much (if any) wayney walnut. They do get some nice and interesting native timbers in there though.
Duffield also get good reports. I haven't visited, may be worth a phone call to see what they do.
For dining table slabs of walnut you are going to have to pay. I would be more interested in finding a good place that knows what they are doing than trying to find the cheapest possible example. Personal opinion, but I think the hidden gems are brown oak and elm which may be a bit easier to source and are beautiful. They are also much rarer in the shops, I could go to Argos and get "walnut" furniture (I know that it isn't) but tiger oak, brown oak etc no chance! To get those the furniture has to be hand made.