This description definitely sounds like Dobell's after it relocated to Tower Street.
It probably mentions in in the NY Times article (I didn't read all of it) but Asman's was in New Row, a small street off St. Martins Lane.
The woman who ran it after James Asman retired, and moved to Mole with it, was called Maureen.
When Ray's moved from New Oxford St. to Shaftesbury Avenue, it was actually in both Shaftesbury Avenue and Monmouth St. You could walk in one side and out the other.
Monmouth St. is an extension of St. Martins Lane (actually Upper St. Martins Lane). I just mention this in case anyone was confusing Monmouth St with St. Martins Lane.