Nearly 30 people who were diagnosed had recently travelled from countries affected by the virus.
Since Tuesday, a further 3,000 people have also been tested for coronavirus.
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.
"The total number of confirmed cases in England is now 80.
"Following previously reported confirmed cases in Northern Ireland, Wales and Scotland, the total number of UK cases is 85."
In Scotland, two more people have been diagnosed with coronavirus, it has been confirmed.
Health Secretary Jeane Freeman said she could not say yet if the new cases of Covid-19 were linked to the first one north of the border, in Tayside.