Mary Agyapong, 28, died after giving birth in April at Luton and Dunstable Hospital, where she also worked.
Her husband told the inquest into her death that he strongly believed Ms Agyapong caught the virus at work.
The coroner concluded Ms Agyapong died of multiple organ failure and Covid-19.
Coroner Emma Whitting said: "As a society, it is important that we learn from all of the lives that have been lost as a result of this terrible pandemic and to consider the wider policy implications that may be lost from each and every one of these.
"Since this is a process which goes far beyond a coroner's inquest and the Prime Minister has indicated his intention to hold a full public inquiry into the Covid-19 pandemic, I urge him to proceed with this as soon as practicable."
She was admitted to hospital with breathing problems on 5 April and discharged the same day.
Dr William Manning, who assessed the nurse on her admission, said he "suspected she had Covid-19" but sent her home as she did not require oxygen therapy.
"She didn't seem particularly happy to go home," he said.
Two days later she was readmitted with Covid symptoms.
Surgeons safely delivered her baby, also named Mary, by Caesarean section on 7 April.
The next day Ms Agyapong was transferred to intensive care, where she died on 12 April.
Mr Boateng told the inquest the mother-of-two felt pressured to work despite being "very concerned about the situation involving Covid-19".
He said his wife would shower as soon as she came home and began sleeping in the spare room to protect him and their son.
"I wanted her to stay at home," he said.
"But due to high demand at the hospital, she had to continue working."
A senior colleague said she had no knowledge of Ms Agyapong being pressured to return or remain at work.
Delivering a narrative conclusion, the coroner said: "The deceased died after contracting Covid-19, but it remains unclear where and when her exposure to the virus had occurred."
David Carter, chief executive of the Bedfordshire Hospitals NHS Foundation Trust, described Ms Agyapong as a "fantastic nurse" who was "highly valued".
"We are reassured that the coroner has found no areas of concern regarding our support for, or care of Mary, and I would like to pay tribute to our staff who did everything they could for Mary in hugely challenging circumstances," he said.
After the ruling, Mr Boateng said the loss of his wife had been "the hardest pain to bear".
"Mary was strong, capable, vibrant, full of life and the most precious person in my life," he said.
"It is still difficult to believe that she lost her life to the Covid-19 virus."