Video report by ITV News Science Editor Tom Clarke
The jump is a significant one - up more than 30 in just 24 hours - and could hasten the moment when officials change how the disease is being dealt with.
Two further positive Covid-19 cases have been detected in Northern Ireland as the latest figures represent the biggest day-on-day increase.
England's chief medical officer, Professor Chris Whitty, said: "As of 9am this morning 32 further patients in England have tested positive for Covid-19.
"Twenty-nine patients were diagnosed who had recently travelled from recognised countries or from recognised clusters which were under investigation.
"Three additional patients contracted the virus in the UK and it is not yet clear whether they contracted it directly or indirectly from an individual who had recently returned from abroad. This is being investigated and contact tracing has begun."
Virologist Dr. Nathalie MacDermott highlighted the three whose source of infection is unknown as a concern.
She said: "It's appropriate for people to start to be concerned when they start to see a significant number of increased cases of coronavirus in the UK.
"We have to remember that a large proportion of those are people who have travelled overseas, the ones that we need to be concerned about are where we can't identify the source of infection here in he UK.
"And so there is the possible risk that others may have come into contact with that source individual."
He announced the emergency coronavirus legislation in the Commons, but it is unclear if the latest change will apply to self-employed workers or anyone on zero-hour contracts.
Mr Johnson said: "If they stay at home and if we ask people to self-isolate, they may lose out financially.
"So, I can today announce that the Health Secretary will bring forward, as part of our emergency coronavirus legislation, measures to allow the payment of statutory sick pay from the very first day you are sick instead of four days under the current rules, and I think that's the right way forward.
"Nobody should be penalised for doing the right thing."
The Government had been under pressure to introduce measures to compensate employees who are following health advice in not turning up for work.
Labour leader Jeremy Corbyn welcomed the announcement but pressed the prime minister on whether it would apply to workers not entitled to statutory sick pay so they would not have to make the "terrible choice between health and hardship".
Mr Johnson said he was "very much aware" of issues faced by the self-employed and those on zero-hours contracts, adding that "some of them will be entitled to statutory sick pay, a great many".
He said ministers were "urgently looking" at the application process for social security payments, when asked by Mr Corbyn if there would be protection for claimants who faced sanctions for missing appointments.
Two further cases were confirmed in Scotland overnight, bringing the number of Scottish cases to three.
The latest cases in Scotland are in Ayrshire and Grampian and are "clinically well and receiving appropriate clinical care", the Scottish Government said in a statement.
One patient had recently travelled to northern Italy and the other had contact with a known positive case.
Medics are gathering details of the places the patients have visited and people they have been in contact with and said those at risk of infection will be contacted by health protection teams for further advice.
Meanwhile, a hospital worker is one of two people in Cumbria who has tested positive for coronavirus.
The healthcare worker is a member of staff at Carlisle's Cumberland Infirmary and is self-isolating after returning from a trip to northern Italy.
The North Cumbria Integrated Care NHS Foundation Trust said the staff member had not been in contact with any patients.
A spokesman said the trust was continuing to operate as normal.
Colin Cox, director of public health at Cumbria County Council, said the council was working with Public Health England (PHE) to get in touch with anyone who had been in contact with the two people affected.
England’s chief medical officer said there is now onward transmission between people in the UK – which could lead to spiralling numbers – although only two cases of this nature have been identified so far.
But Professor Chris Whitty said it is “very unlikely” the UK will need to shut down cities.
He said the NHS would cope with a major spread of cases but could come under “very high pressure” in a large epidemic and there could be “several weeks which could be very difficult” for the health service and wider society.
Prof Whitty told BBC Breakfast there could be a need to do “extreme things” to protect the elderly and those with pre-existing health conditions.
Coronavirus developments around the world
Italy's education minister says teaching activity will be suspended 'outside the red zone' until March 15 following the Covid-19 outbreak.
The Italian government has ordered all sporting events to take place without fans until April 3 due to the coronavirus outbreak.
In Iran, 23 members of the country's parliament and head of the emergency services were reported to have been infected. Iran said the disease has killed 92 people, amid 2,922 confirmed cases, and Friday prayers were cancelled across all provincial capitals
South Korea confirmed another 142 cases on Wednesday morning, raising its total to 5,328, the second-highest in the world.
Saudi Arabia banned its citizens and residents from performing the Muslim pilgrimage in Mecca, expanding on a ban implemented last week on foreigners visiting Mecca and Medina.
In Spain’s Basque region, at least five doctors and nurses were infected and nearly 100 health care workers were being held in isolation
Infections in the US topped 100 and the death toll climbed to nine, all in Washington state
The number of countries hit by the virus exceeded 70, with Ukraine and Morocco reporting their first cases
France’s president announced the government will take control of current and future stocks of face masks to ensure they could go to health workers and coronavirus patients
Worldwide, more than 93,000 people have been infected and over 3,100 have died, the vast majority in China
The mushrooming outbreaks around the world contrasted with optimism in China, where thousands of recovered patients were going home and the number of new infections has been dropping.
In China, the count of new cases dropped again Wednesday to just 119. It is still by far the hardest-hit country, with more than 80,000 infections and about 95% of the world’s deaths.
“We scrutinised this data and we believe this decline is real,” said WHO outbreak expert Maria Van Kerkhove, who travelled to China as part of a team from the UN agency.
She said the extraordinary measures taken there, including the lockdown of more than 60 million people, had a significant effect on the direction of the outbreak.
“We believe that a reduction of cases in other countries, including Italy, Korea, Iran, everywhere, that this is possible,” she said.