Education secretary said teachers were among public sector workers set to face "pay restraint".
The health minister's comments have been described as "contemptuous" by unions who say proposed award is a "kick in the teeth".
Philip Rutnam quit as permanent secretary claiming constructive dismissal amid bullying allegations.
The chancellor has frozen pay below inflation for more than a million public sector workers.
"A pay freeze would be an outrageous attack on some of the workers who sacrificed the most during the pandemic", the GMB union said.
It is believed to relate to the leaking of diplomatic cables that led to the resignation of Lord Darroch last year.
Steve Reed tells HuffPost UK: “The more we move towards a politicised model... the more will go wrong, and I think that’s what we’re seeing."
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Nurses were excluded from the wage increase for around 900,000 public sector workers announced in July.
There are also growing signs of a civil service walkout over his plan to break international law and unpick his own exit deal.