Should have added the 1938 LOC Catalog of Copyright Entries seems to attribute it to R.C.Clarke (I think!).

The BL catalog entry for a recording has the following interesting details:

Title: Bertie the bounder
Contributor: Grossmith, George, Jnr (singer, male)
Notes:
Item: Label: Clarke;
Item: The show "Our Miss Gibbs" was jointly composed by Lionel Monckton;
Item: and Ivan Caryll.;
Item: This song is listed as being part of that show but as no composer;
Item: called "clarke" is mentioned in connection with it, it has been;
Item: assumed that the song was composed separately and later;
Item: incorporated.
Holdings Notes: Re-issue of 78 rpm disc probably Gramophone 02255.
Shelfmark(s): 2LP0070306 S 1 BD 2; 1LP0148074 S 1 BD 2


Mick