The '2 Men' are David Steele (b. September 8, 1960) and Andy Cox (b.January 25, 1956), both at the time members of Fine Young Cannibals
. They first recorded together as members of Birmingham (UK) ska band Beat, The (2)
The 'Trumpet' is Graeme Hamilton.
Note that Two Men And A Drum Machine
exist as a separate artist (without A Trumpet).