Keir Starmer, the newly elected leader of the Labour Party said: "Wishing the Prime Minister well and a speedy recovery."
Nicola Sturgeon, Scottish First Minister said: "Wishing the PM all the best and a speedy recovery."
And Sadiq Khan, Mayor of London, said: "Sending my very best to the Prime Minister and wishing him a swift recovery."
GP Dr Sarah Jarvis told the BBC it is likely the Prime Minister has "moderate" symptoms of coronavirus.
"The majority of people who develop coronavirus will have mild symptoms - that's probably 80 per cent or so," she said. "The older you become the more likely it is that you will become severely unwell with this.
"There is a severe stage, a moderate stage and a critical stage."
Jarvis, who is not Johnson's doctor, added:
"Given he is staying in charge of the Government, that suggests to me that he probably has moderate disease but that, as a precaution, he is being taken in to check the oxygen levels in his blood, to do X-rays and probably scans of his chest.
"And to do blood tests to see for instance what his white cell counts look like and what his liver functions look like."
Jarvis said of Boris Johnson's hospital admission: "The main focus is going to be on his lungs.
"The majority of people are going to progress to have inflammation of the lungs and that inflammation can result in damage to lung tissue, but also importantly can prevent oxygen being transferred into the blood stream."
She said the tests themselves are very rapid.
"You can clamp a monitor on to somebody's finger and that will give you a test very quickly, in fact in general practice we have systems set up where people who have been discharged from hospital are having those tests delivered to them and they just pop the monitor on to their finger and literally within 30 seconds it will give a result.
"The X-ray will take a little longer and the scan will need to be assessed and looked at by a consultant - we are certainly talking a couple of hours I would say."
Dr Rupert Beale, Group Leader, Cell Biology of Infection Laboratory, Francis Crick Institute, said:
"Doctors will be monitoring important vital signs such as oxygen saturations. They will also check blood tests to see what the immune response to the virus looks like, and to assess liver and kidney function.
"They will perform an electrocardiogram (ECG) to check the heart. More sophisticated tests may include a CT scan of the chest to get an accurate picture of the lungs. They will consider the best way to deliver oxygen, and will also consider other treatments depending on test results.
"We are in a struggle between humanity and a deadly virus. Whatever your politics, we are all on the same side. I wish the Prime Minister a speedy recovery."
Q&A: BORIS JOHNSON IN HOSPITAL
Why has Johnson been taken to hospital?
The Prime Minister was transferred to hospital as a "precautionary measure" on the advice of his doctor, according to Number 10. Ten days after his positive test for Covid-19, Johnson is still suffering a high temperature.
Who is leading the Government?
When the Prime Minister first announced that he was ill last week, it was said that the Dominic Raab, Foreign Secretary, would take over if Johnson became too sick to work. A spokesman insisted tonight that Johnson remains "in charge of the Government" despite his hospital admission.
Has Johnson been working since his diagnosis?
Johnson has led several meetings via video conferencing since his diagnosis including the Cabinet. He has shared several video updates from his Number 11 flat and stepped outside to join the nationwide clap for NHS staff on Friday NZT.
Has his pregnant fiancee been ill?
Carrie Symonds said she had been suffering Covid-19 symptoms, but is "on the mend". Symonds, 32, who is expecting the couple's first baby in the early northern summer, said she was not tested for the virus.
Has anybody else in the Government been ill?
Matt Hancock, Health Secretary, is already back at work after having tested positive for the coronavirus. Scotland Secretary Alister Jack also developed telltale signs of the illness. Chief medical officer Professor Chris Whitty self-quarantined after he noticed symptoms, and the Prime Minister's chief adviser, Dominic Cummings, also self isolating.
