Doctors' Commons was the host to various London courts, so to find cases held there the best approach is to look at the archive for the court where the case was in process, rather than for Doctors Commons.
From the description, it looks like the case you have is probably from the London Consistory Court. The records are in the LMA under DL/C. The archive has a fine collection of depositions, which can go into an extraordinary level of detail. If you are lucky (and if the dispute got that far), these will survive for your case.