The following is an attempt at listing some of the Oriole series. 
First the fifteen 1927 records:

Now the early 1930s P-series: Grateful thanks to Steve Walker for filling all the gaps. See also notes at the bottom of the page.

Finally, the mid-1930s LV-series; these appear to have been re-issued in the 1940s in the LB series, then in the 1950s on the CB-series.

Oriole Private Recordings: It is reasonable to assume that Levy's produced many of these, probably hundreds, but generally only single copies have been found of those known, excepting the Vernon's Pools record, so it it not unlikely that Levys only pressed individual copies of most private recordings. I will attempt to list them below, hopefully in master number order, though not all show a master number, so some guesswork has to be undertaken. These are usually single-sided, often with the Oriole-stamped backing. One or two show "catalogue number" in an SP-series on the label, though I don't believe they were ever publicly available in that way. Where known, I will show this.
Thanks to the following people who have helped with this listing: Colin Bray, Norman Field, Charles Hippisley-Cox, Mike Langridge, Alan Miles, John Norman, and most of all, Steve Walker.

Note: A copy seen of 906/907 (the sides are coupled) says there were only 18 copies made of this record (hand-written on the label)

NOTES regarding the Oriole P-series and Levys by Steve Walker. (dated October 28, 2012)

All details are taken from the original labels, with the exceptions of  P-103, 108, 109, 112, 114 and 115. Note that P-114 is a 12” record. Masters in italic face are hand-written, and were recorded in an upstairs room of the Regent Palace Hotel; masters in upright face are type-set and were recorded in Levy’s own studio at Rosslyn House, Regent Street (but see note on the Adelaide Hall session, below). 

These records seem to have been issued in two blocks: P-100 - 109 in the autumn of 1931, and P-110 - 114 in the autumn of 1932; only P-113 and P-114 were ever publicly advertised so far as I know. All originally had silver labels with black printing; the most popular were re-pressed on gold labels with black printing, and these re-pressings appear to date from 1933-34. A batch of P-107 on silver is known to have been sent to the Liberty Music Shop in New York; exact recording dates where known are likely to have come from test pressings.

The second Harry Roy session was moved in Rust & Forbes' BRITISH DANCE BANDS ON RECORD to the spring of 1932, on the understandable but erroneous evidence of the general release date of some of the tunes in England. The band in fact gave up doubling at the Bat Club in November, 1931, under the pressure of mounting the full band’s stage show at the RKO Theatre, Leicester Square. It is likely that the band got advance copies of the sheet music from Paris, where the release restrictions did not apply, and that the sales of the Oriole records were so limited as to escape the attention of the Performing Rights Society.

The Adelaide Hall session, however, bears faint stylo-written masters prefixed R-, indicating that they are genuine English Brunswick masters. The only explanation I can offer is that Brunswick were allowed the use of Levy’s small Rosslyn House studio on occasions when their normal venue  -  Chappell’s Aeolian Hall in Bond Street  -  was too large for the purpose; Brunswick 1217 must have been issued contemporaneously with Oriole P-102 and 103, though Brunswick 1307 is a 1932 re-issue. To make matters worse, some later pressings of the Oriole P-100 series bear ‘Buckingham’ stamper codes, indicating that they were pressed by Decca at New Malden. It cannot be stressed too strongly that the master series of Oriole and English Brunswick do NOT interlock, as was once believed, though they are numerically and chronologically very similar. The note which appeared for many years in Adelaide Hall’s chapter in Brian Rust's JAZZ RECORDS regarding master 231 is correct in what it records, but it is of no relevance in that context; it is a 12” Oriole master.

Collector and sound restorer (and jazz musician) John R.T. Davies was the first to point out (and I entirely agree) that the studio used pre-numbered waxes, thereby accounting for many blanks by using a new number for each take. This is supported by the existence of a number of rejected takes in test pressing form, which I have of course not included in the listing.

P-115 is a complete rogue, but the report appears to be correct (which is to say it does not seem to be a mis-report for an SP- or SR- issue; it was filed in order at THE GRAMOPHONE). It is likely to be on orange with gold printing, but I have not seen it.