While shops have reopened, pubs and restaurants are only permitted to serve customers outside, with the current rules remaining in place until 17 May at the earliest.
However, the weekly registered deaths involving coronavirus in England and Wales have remained at the lowest level for more than six months, with the Easter break affecting numbers, according to the Office for National Statistics (ONS).
It comes as "extraordinary" real world data showed that 32 vaccinated people were hospitalised with COVID in recent months, according to The Telegraph.
Last week the UK had the lowest cases of COVID in Europe, while the overall number of deaths registered in the week to 9 April in England and Wales was below the five-year average for the fifth consecutive week, the ONS said.
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For the first time since September, the latest figures showed also fewer than 2,000 COVID patients in hospital.
The government has said there will be a minimum of five weeks between each set of restrictions easing, to give it time to assess the impact on public health.
Lockdown easing will also depend on the vaccine rollout continuing smoothly and evidence the vaccine is reducing hospital admissions and deaths.
On Tuesday, the prime minister insisted the “path to freedom” remained open, and said there was nothing in the figures to suggest a deviation from the path out of lockdown – but did not suggest that the government would speed it up.
Acknowledging soaring cases overseas and warnings from scientists that there will be another wave this year, Johnson said: “As we look at what is happening in other countries, with cases now at record numbers around the world, we cannot delude ourselves that COVID has gone away.
“I see nothing in the data now that makes me think we are going to have to deviate in any way from the roadmap – cautious but irreversible – that we have set out.
“But the majority of scientific opinion in this country is still firmly of the view that there will be another wave of COVID at some stage this year.
“And so we must, as far as possible, learn to live with this disease as we live with other diseases.”
Earlier this month, Dr Mike Tildesley, a member of the Scientific Pandemic Influenza Group on Modelling (Spi-M), which advises the government, said a case could be made to quicken the easing if COVID numbers continue to fall.
Speaking to LBC Radio, Tildesley, a professor of infectious disease modelling at the University of Warwick, said: “If things keep going down at the rate that they are then there certainly is an argument for speeding up the process.”
He added: “I was really pleasantly surprised that with schools open we have managed to keep things in check.
“If these numbers keep going down over the next few weeks there certainly is an argument to say, ‘Well, actually we’re doing really well with the roadmap, it could be sped up.’”
Watch: How England will leave lockdown