The private health company Circle took over Hinchingbrooke Hospital Trust in Cambridgeshire six mnoths ago.
Karen Jennings, assistant general secretary of Unison, said it was right that Hinchingbrooke "celebrates these very early successes" but there were "early signs of concern" over cuts to cleaning staff.
"Staff are a little bit nervous, there are talks about voluntary severance and a large cut in the number of cleaning staff," she told the Today programme.
Get in touch with Today via
or text us on 84844.