Okay: I found an appropriately skeptical review of what's known, vs. what might be possible, about Richard Warren, at http://www.martin-house.com/tng/getperson.php?personID=I0969&tree=Martin
. It lists christenings of Richard Warrens in England between 1570 and 1587, evidently taken from parish registers -- the one at St. Peter Cornhill included -- and makes the point that the decisive, missing data in every case is the christening records of Richard's five known daughters, who were all born in England. So until and unless someone finds a parish with (most of, at least) those five records, at least these 16 options apparently remain in play.
Even given that the 16 records are taken at face value from the IGI, not exactly an authoritative source, the point about the Warren daughters' baptisms is telling.
If however we had anything at all that connected Richard to the skills of the armorer's trade, that would make the St. Peter Cornhill record particularly interesting.