Burley pointed out that the prime minister promised no one would have to sell their homes for social care at the last election.
"I’m only doing what you normally do, but carry on," the health secretary said when the news presenter tried to ask a question.
"If they haven’t got vaccinated by now, then there is an issue with patient safety," the health secretary said.
"I let myself and my viewers down," the presenter said.
"A quick thought before I ask you one more question, because it does look like Mr Opik really does want to talk to you..."
The presenter was taken off air after attending a gathering for her 60th birthday when London was under Tier 2 restrictions.
The presenter did not hold back during an appearance on The Last Leg.
Beth Rigby and Inzamam Rashid will also remain off air for three months.
The Sky News broadcaster admitted breaking safety rules after celebrating her 60th birthday in London.
Host who admitted breaking Covid-19 safety rules says she will be on a pre-planned holiday to Africa.
The Sky News presenter is facing an internal inquiry following the celebration held in Tier-2 London at the weekend.
Health secretary refuses to criticise former Australian PM over his controversial past.
After being told she couldn't pin the blame on the government's scientific advisers, she replied: "Well I can," before swiftly rowing back.
The Funky Friday rapper hit out at the prime minister during a performance at this year's Brit Awards.
At least 2020 can't be any worse, right?
The Conservative said he was doing another interview and "cannot be in two studios at the same time".
Johnson will take part in a head-to-head with Jeremy Hunt on July 9.
Three interviews with young people, three people attacked, interrupted, patronised and dismissed – intimidating our generation to keep us quiet on the big issues will not work
Faisal Islam asked the man, who was wearing a Ukip rosette: 'Why did you just shout treason? How is that helpful?'