I have a ratty old 12 ga hammer double with Birmingham proof marks which predate 1887. It is back action with a side (left) lever opener. Lock plates are marked W Richards. Top rib says W Richards London Laminated Steel. Though it does appear as if was originally a cut above the Belgian W richards guns it is by no means either a Westly Or William Richards. Clabrough may have made it, but it is certainly not the quality of my Clabrough sidelock hammerless & even this one from a catalog I have seen of a close era was near the bottom of the Clabrough line.
Having Birmingham proofs does not automatically make a gun of high quality or from a well known reputable maker. Likewise having Belgian proofs does not automatically make a gun Junk, though I think most guns marked W Richards with Belgian proofs likely are.
Rocdoc/Steve summed it up in his above post. If one can't tell the difference between the normal W Richards & either a William or Westly then they aren't very observant of anything but the name.
