Actually it isn't accurate to attribute "Mr Bloe" solely as Zack either.
"Groovin' with Mr Bloe" (a cover version of the track by Wind) was released by record label DJM (Dick James Music) featuring Zack playing piano alongside DJM house musicians Hookfoot. Hookfoot often backed Elton on his albums for DJM and the original DJM sessions for the single did feature Elton playing piano. The studio were not happy with the end result and chose Zack to rearrange the track. It was at this point that Zack took over piano for the recording. The overwhelming success of the release required "Mr Bloe" (Zack and Hookfoot) to form briefly as a group for appearances on Top of the Pops etc.
As indicated by the link, Mr Bloe and Elton had later collaborations - these collaborations actually comprised Hookfoot playing songs written by Elton, with Elton on piano.
BTW "original" sessions of "Groovin'..." with Elton on piano appeared as part of the bootleg album "I Remember When Rock Was Young"...
http://www.eltonography.com/imports/i_remember _when_rock_was_young.html