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The veteran news anchor has fronted Sky's flagship breakfast show for the past five years.
The Reform UK leader insisted James McMurdock's conviction was now "irrelevant".
Ministers have suggested a 2.8% pay increase, an offer unions have called "deeply offensive".
'No, Stop It': Kay Burley Clashes With Mel Stride Over £715 Million Tories 'Wasted' On Rwanda Scheme
The shadow chancellor blamed Labour for scrapping the policy after the election.
It follows reports that a cabinet minister claims £350 of taxpayer cash per month for her second home's energy bills.
Alison McGovern did not want to get drawn on the issue.
The Sky News presenter told the work and pensions secretary: "I'm hearing the carrot, I'm not hearing the stick."
The PM did not meet the demonstrators or mention them in a speech on Saturday.
At least 11 members of the current UK cabinet have publicly insulted the new US president-elect over the years.
"It's not a great look, is it?" Gareth Barlow said to Wes Streeting.