The prime minister told MPs the legal duty to isolate for those who tested positive would be dropped as he unveiled his "living with Covid" plan.
From 1 April the provision of free testing would be targeted to the most vulnerable, Boris Johnson said.
But the British Medical Association, a doctors' union, said the plan failed to protect those most at risk from Covid.
And opposition parties said the prime minister's blueprint out of the pandemic had moved too fast, and voiced concern over the scaling back of free testing.
The Scottish government said the public health advice it had received did not recommend lifting the restrictions.
Speaking at a Downing Street news conference on Monday evening, Mr Johnson said "today is not the day we can declare victory over Covid because this virus is not going away".
He described the pandemic as "two of the darkest, grimmest years in our peacetime history".
However, he said the nation had passed the peak of Omicron, with falling cases and hospital admissions.
And he said the country could now complete the "transition back towards normality" while retaining contingencies to respond to a Covid resurgence or a new variant.
England's chief medical officer Prof Sir Chris Whitty said the ending of virus restrictions was a "gradual, steady change over a period of time", adding: "This is not a sudden 'everything stops'."
He said the number of people being infected with Omicron was still "very high".
Office for National Statistics (ONS) infection figures last week estimated that one in 20 people in England had Covid.
Sir Chris said the public health advice for people with Covid would still be to self-isolate to prevent others catching it, as it would be for many other highly infectious diseases.
Sir Patrick Vallance, the UK government's chief scientific adviser, warned the virus would continue to evolve over the next couple of years and there was no guarantee that future variants would be less severe than Omicron.
He argued it was crucial the nation retained a virus surveillance system to monitor new threats and the capacity to "ramp up" measures again quickly to protect the vulnerable.