Doctors at an NHS trust were told they don't have to list Covid-19 on the death certificates of coronavirus patients, it is claimed.
The Good Law Project said it has obtained a leaked document telling medics that recording "pneumonia or community-acquired pneumonia" as the direct cause of death was acceptable.
The unnamed trust's guidance contradicts that issued by the Government, which says Covid-19 is an "acceptable direct or underlying cause of death" on a death certificate.
The Good Law Project said coronavirus deaths could be going unreported, lowering the official toll reported to the public, if doctors do not follow the Government's guidance.
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It said: "If doctors are not required to write Covid-19 anywhere on the death certificate, then we have no way of knowing if those figures are correct."
It did not identify the trust.
The organisation fights cases "that defend, define or change the law" and challenges "abuses of power, exploitation, inequality, and injustice".
A spokesperson said: "Leaked guidance from an NHS hospital trust reveals that doctors are not being required to report Covid-19 as the cause of death for patients."
The group claims the guidance from the trust states: "‘Doctors are asked to use the standard MCCD (Medical Certificate of Cause of Death) form to certify death. ‘Pneumonia ‘or ‘community acquired pneumonia’ are acceptable at 1(a) on the MCCD.
"There is no requirement to write COVID 19 as part of the MCCD. It may be mentioned at 1(b) on the form, should the doctor wish.’"
The Good Law Project said the document states Covid-19 may be mentioned in a different section of the form relating to indirect causes of death "should the doctor wish".
But the guidance then repeats that pneumonia, a complication of the new strain of coronavirus, can be written down.
The Good Law Project has instructed lawyers to send a letter to the hospital trust asking it to withdraw the guidance "urgently".
It has also started a petition calling on Health Secretary Matt Hancock to ensure all Covid-19 deaths are "recorded and reported properly".
"He should investigate what advice is being given out to doctors by all hospital trusts," the organisation added.
A spokesman for the Department of Health said: "This appears to be an altered version of official guidance.
"Guidance from the UK Government is clear that 'Covid-19 is an acceptable direct or underlying cause of death for the purposes of completing the Medical Certificate of Cause of Death'."
A spokeswoman for NHS England said: "The circulating document forwarded to you by The Good Law Project appears to be a trust’s interpretation put into writing.
"It is not ours, nor is it official, and we do not know which trust it has come from."
Earlier this week, concerns were raised that medics and GPs were allegedly failing to record Covid-19 on death certificates.
A whistleblower working in southern England told Channel 4 News that some doctors were putting long-term conditions such as dementia as the cause of death even if they suspected coronavirus.
As of 5pm on Wednesday, 13,729 people have died in UK hospitals after contracting coronavirus, according to the Department of Health.
Thousands more are feared to have died in care homes, private homes and hospices.
As of 9am on Thursday, 103,093 people have tested positive for coronavirus in the UK.
The true total is believed to be higher as many people displaying symptoms are not being tested.
