The two patients have been described as older people who were being treated for underlying health conditions.
Confirmation of the deaths came after the UK government reported 74 new cases of Covid-19 on Wednesday, bringing the total number of cases in the country to 456.
"The Trust can confirm that a patient in their 70s being treated for underlying health conditions has died," Diane Wake, chief executive of the Dudley Group NHS Foundation Trust, said in a statement.
Dr Catherine Free, medical director at George Eliot Hospital NHS Trust, confirmed an elderly patient who was being treated for "a number of serious underlying health conditions" had also died.
The families of the two patients have been informed of the deaths, NHS England said.
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In a statement, chief medical officer Professor Chris Whitty said: "I am sorry to confirm a seventh and eighth patient in England who tested positive for Covid-19 have sadly died.
"I offer my sincere condolences to their families and friends and ask that their privacy is respected."
Matt Hancock, the health secretary, said on Wednesday evening that he had invited the Labour Party to meet with him tomorrow morning to discuss emergency legislation for the outbreak which will be set out next week.
Mr Hancock said the legislation would help the "national effort to keep vital public services running" to support businesses, with adult social care at the "frontline" of the response.
"I know how worrying this is, I know people have deep concerns, I know everyone will play their part in this national effort to defeat the virus," he added.
"The best way to beat it is for us to work together and we'll do whatever it takes, we'll give the NHS whatever it needs and we'll do all that we can to keep people safe and get through this together as a parliament and as a nation."
Additional reporting by PA
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