Mr Hancock was sat next to Boris Johnson on the Government frontbench as the premier was grilled by the Labour leader.
Sir Keir demanded answers on the Government’s plans for coronavirus testing in care homes.
But he was repeatedly talked over by a seated Mr Hancock, resulting in a furious telling off from Sir Lindsay.
The Commons Speaker initially said he did not ‘mind you advising the Prime Minister’ but told him to be quiet when Sir Keir was speaking.
Mr Hancock then protested prompting Sir Lindsay to hit back and ask the Health Secretary: ‘Sorry – do you want to leave the chamber?’
Sir Lindsay Hoyle today threatened to kick Matt Hancock out of the House of Commons after the Health Secretary repeatedly challenged Sir Keir Starmer during PMQs
Mr Hancock could be heard talking over Sir Keir as the Labour leader tried to ask Boris Johnson questions. Sir Lindsay told the Health Secretary: ‘Sorry – do you want to leave the chamber?’
Sir Keir used PMQs to challenge Mr Johnson on the Government’s approach to tackling the spread of coronavirus in care homes.
The Labour leader cited evidence given by care bosses which suggested that while ministers had pledged to ramp up testing staff and residents they were yet to actually deliver on it.
Sir Keir said the Government’s own documents state every care home for over-65s will have been offered testing for residents and staff by June 6.
Mr Hancock could be heard challenging Sir Keir on what he said, as the Labour leader addressed him directly: ‘The Health Secretary says “he is wrong” – I am quoting the Government’s paper.’
Sir Keir then asked the PM what was causing the ‘continued delay in routine testing in our care homes’.
Mr Johnson accused Sir Keir of being ‘simply in ignorance of the facts because the reality is already 125,000 care home staff have been tested’.
The Prime Minister then praised Mr Hancock and said thanks to the hard work of the Health Secretary the Government will soon be able to conduct 200,000 tests a day.
Mr Johnson said ‘actually now this country is testing more than virtually any other country in Europe’.
When Sir Keir replied, he accused the Prime Minister of failing to answer his question as Mr Hancock continued to talk over the Labour leader.
Sir Lindsay then interrupted proceedings and said: ‘Order, order. Secretary of State for Health, please.
‘I don’t mind you advising the Prime Minister but you don’t need to advise the Opposition during this.’
Mr Hancock appeared to try to plead his case to the Commons Speaker, prompting Sir Lindsay to threaten to kick him out of the chamber.
Sir Lindsay said: ‘Sorry – do you want to leave the chamber? We are on maximum numbers, if you want to give way to somebody else I am more than happy.’
The current ‘hybrid’ arrangements in the House of Commons mean a maximum of 50 MPs are allowed to be physically present in the chamber so that social distancing rules can be adhered to.
The telling-off comes a matter of weeks after Mr Hancock was accused of sexism for telling a female Labour MP to ‘watch her tone’.
Sir Keir and Mr Johnson repeatedly clashed over the Government’s approach to tackling coronavirus in care homes
Dr Rosena Allin-Khan, a former Labour deputy leader candidate who also works as an A&E doctor in the fight against the pandemic, had said the government’s approach to the outbreak had ‘cost lives’.
In response, an indignant Health Secretary told the Labour MP that she should ‘take a leaf out of the shadow secretary of state’s book in terms of tone’.
Dr Allin-Khan, who attends shadow cabinet meetings as the shadow minister for mental health, shared the exchange on social media and later tweeted she would not ‘watch her tone’ when challenging the Government.
The Health Secretary’s comment sparked uproar among some MPs, with former acting Labour Party leader Harriet Harman branding it ‘creepy’.
Mr Hancock has been one of the key players in the Government’s coronavirus response, frequently taking charge of Number 10 press conferences and making major announcements.
But he has faced intense scrutiny over his handling of key issues, including testing, care homes and Personal Protective Equipment.
He is thought to have had a furious bust-up with Mr Johnson in recent weeks, raising questions over his Cabinet future.
There have been a string of embarrassing Government failures over the supply of PPE with senior sources suggesting Mr Hancock is ‘on borrowed time’ in the Cabinet.
One source claimed Mr Johnson had raised questions with Mr Hancock about his department’s grip on the crisis, only for the Minister to plead: ‘That’s not fair – give me a break.’
On the issue of testing he was repeatedly attacked by Tory MPs for promising to hit a target of 100,000 tests carried out every day by the end of April.
It subsequently emerged the target was not recommended by the Government’s panel of scientific experts.
The Health Secretary then claimed at the end of the month that he had hit the target.
But the statistics showed home testing kits had been counted on the day they were put in the post rather than when they were actually processed.
In recent days he has faced growing pressure over the bungled roll-out of the NHS coronavirus contact tracing app.
On May 12 the Health Secretary had said ‘we’re rolling out in mid-May’ but yesterday he refused to set a date as Downing Street would only go so far as saying it would be made available nationwide in the ‘coming weeks’.
The app is currently being trialled on the Isle of Wight and it is viewed as an integral part of the Government’s ‘test, track and trace’ programme which will help to prevent a second wave of the deadly disease.
Some in Whitehall believe Mr Hancock, pictured alongside Boris Johnson in November 2019, is being lined up as a ‘fall guy’ for the government’s coronavirus failings
Number 10 has insisted it is ‘possible’ to do contact tracing without the app but many experts believe the UK will struggle to get back to normal without the technology being in place.
Meanwhile, there are growing questions over why the Government chose to develop its own app when other countries have adopted one put forward by Apple and Google.
Mr Hancock has also faced accusations of prioritising the NHS over care homes at the start of the outbreak with care workers claiming to have been treated like ‘second class citizens’.
It was reported in April that Mr Hancock was being lined up as the ‘fall guy’ for the Government’s coronavirus failures.
Inside sources said Mr Hancock had ‘not had a good crisis’ while a former Cabinet minister claimed some in Whitehall believed the Health Secretary had developed ‘a sort of Messiah complex’.
Some believe Mr Hancock will be from the Department of Health before a widely-anticipated future inquiry is held into the Government’s response to the outbreak.