The figure, accurate as of 9am today, is up by 149 cases from Wednesday's update.
Sheffield is the worst-hit local authority area, with 1,412 confirmed cases, followed by Leeds with 743 confirmed cases.
In the UK, 103,093 people have now tested positive for Covid-19.
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Downing Street has said the UK now has the capacity to conduct 35,000 coronavirus tests a day - although fewer than half that number are currently being carried out.
The Prime Minister's official spokesman said that in the 24 hours up to 9am on Wednesday, 15,994 tests were carried out across England, Scotland and Wales.
"We have been very clear that where there is spare capacity available that should be used on NHS staff, on their families, and in social care," the spokesman said.
The full list of confirmed cases by local authority area are as follows:
Barnsley - 415
Bradford - 460
Calderdale - 168
Doncaster - 239
East Riding - 272
Hull (Kingston upon Hull) - 175
Kirklees - 381
Leeds - 743
North East Lincolnshire - 86
North Lincolnshire - 142
North Yorkshire - 542
Rotherham - 407
Sheffield - 1,412
Wakefield - 344
York - 153
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