Although Max Goldberg worked as a regular freelancer for Bert Firman (and later on John Firman) I think the hot trumpet work here sounds more like Jack Jackson, who has just joined Jack Hylton's Orchestra but was apparently moonlighting as a freelance studio musician as well! For comparison, listen to Jack Jackson's equally excellent playing on the following Fred Elizalde track from August-September 1927:-
Jackson seems to be under the influence of both Bix and Red Nichols. As time went on, Bix became a stronger influence.
Incidentally, Brian Rust changes his mind about the hot trumpeter on the Firman side. In British Dance Bands On Record, he lists the trumpet section as "Frank Guarente and another", whereas in Jazz Records (6th Edition) he lists "Max Goldberg and another"!
By the way, the trumpeter on the Firman side can't be Henry Levine - as some have suggested - because Levine had already gone back to the States by the time "Ain't That A Grand And Glorious Feeling?" was made.