It's way back in the mists of time that I had a frame with the Anstey setup. I gave myself the problem with the brake locking on 'full bump' by first setting it up with 'downward lever' so I well remember that particular point. As I recall (hazily!) I didn't replace any components, so I'm racking the old brains a bit to come up with something useful.
As a first check, if you screw the fulcrum adjuster right in can you lock the wheel ? (If it doesn't I think that shows something is wrong on the 'inside'.) Otherwise, is it possible to turn the lever round and would that make any difference?
'55 Huntmaster, '56 VH, ' 51 VH, '80 R100RT, '00 Sprint ST (but all those Ariel parts can only make one running bike...)