Let me know if you go, I'll come take piccies for you
Whitehall farm is lovely but its quite a trek down to the beach (from memory it took us 1 hr 45 mins each way) but its mostly off road on permissive tracks, Mill farm takes horses & campers/lorries but not sure if they do B&B but being in wells I bet you could find somewhere easy enough if they don't Those are the only 2 places I know to stay within riding distance of Holkham beach.
Holme beach is just around the coast a little, that's where we stayed last, at Courtyard Farm. There is also Home Farm which is B&B and right in Holme village so maybe 5 mins onto the beach.
I personally prefer Holkham beach to ride on, its bigger and more deserted (the Burnham end is a nudist beach so not so busy), but there isn't much in it in terms of riding. We now tend to stay near Holme when we go, because the non-beach riding is better and the beach is closer to where we can stay. When we day trip we always go to Holkham though.