There evidently were several records featuring the anonymous Savoy Players and Orchestra. They are listed below, but I have very little information about them.

According to the Varsity-GramophoneConcertone Discography, Gramophone 2061 consists of the following

(2061A)

The Mikado parts 1 and 2
Gondoliers parts 1 and 2

(2061B)

Iolanthe (Sentry Song) parts 1 and 2
Iolanthe (vocal gems)
Yeoman [sic] of the Guard parts 1 and 2
Pinafore

According to correspondent Tony Dwyer, Halo 5061 contains the following excerpts from The Mikado:

Overture
A wandering minstrel
Our great Mikado
The Lord High Executioner
Taken from a county jail
I've got a little list
A more humane Mikado
The criminal cried
The flowers that bloom in the Spring
Tit-willow
There is beauty in the bellow of the blast
Finale

Tony added that "patriotic" has a long 'a' in "A wandering minstrel." In "The flowers that bloom in the spring," Nanki-Poo inserts a cadenza, and Ko-Ko imitates it. He added:

It would be presumptious of me to "review" this record; I'm nowhere near an expert on G&S. It strikes me as a budget recording, but I found the performances entertaining, although my copy of the record has definitely seem better days.

From Tony's report, this seems to be a fairly substantial recording of The Mikado, but I have elected to leave it listed here, with the other pressings that appear to come from the same series.

It is not clear whether the item I have listed as the Halo Pinafore is also part of the series. Another correspondent has alerted me to a further Halo issue, #50308, that seems to be a companion to the Halo Pinafore and has different contents to those Tony has described. A pretty mess indeed!