Dr Chaand Nagpaul, chairman of the British Medical Association, said easing restrictions was not an “all or nothing” decision.
He said “sensible, cautious” measures will be vital to minimise new waves of coronavirus and keep the country from slipping back into lockdowns.
Under the current plan, July 19 would see all legal limits on social contact lifted and large venues opened.
The easing of restrictions was moved back a month from June 21 because the highly contagious Delta variant was sweeping the country and too few people had been vaccinated.
Senior members of the government, including Prime Minister Boris Johnson and new Health Secretary Sajid Javid, have indicated their confidence that the July 19 date will be met.
The BMA wants people to carry on wearing masks in enclosed public areas, including public transport and shops, and to promote social distancing and meeting outdoors wherever possible.
“As case numbers continue to rise at an alarming rate due to the rapid transmission of the Delta variant and an increase in people mixing with one another, it makes no sense to remove restrictions in their entirety in just over two weeks' time,” Dr Nagpaul said.
“The promise was to make decisions based on data and not dates, and while we were pleased to see the government react to data in delaying the easing on June 21, ministers must not now simply disregard the most recent, damning numbers by rushing into meeting their new July 19 deadline.
“Everyone appreciates the efforts and sacrifices we have all made so far to suppress the spread of the virus, and it would be tragic if we were to undo this good work now,” he added.
Public Health England figures show 161,981 confirmed and probable cases of Delta variant have been identified in the UK – up by 50,824, or 46 per cent, on the previous week.
The Delta variant, first identified in India, now accounts for approximately 95 per cent of confirmed cases in the UK.
And latest figures from the Office for National Statistics show one in 260 people in England had Covid in the week to June 26. That is up from one in 440 in the previous week and is the highest level since the week to February 27.
Dr Nagpaul said that, while hospitalisations remained low compared to the rise in cases, numbers were “increasing at pace” with twice as many Covid patients in beds and on ventilators than this time last month.
“Even if people aren’t getting admitted to hospital at the same rate, spiralling levels of community transmission provides a fertile ground for new, potentially vaccine-resistant variants to develop,” he said.
The BMA’s recommendation comes amid reports that ministers plan to drop all legal requirements including self-isolation for fully-vaccinated people who come into contact with someone who is infected.