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During a campaign visit in Hartlepool, the prime minister told reporters: "I think we've got a good chance, a good chance, of being able to dispense with one-metre plus."
He stressed the move would be "dependent on the data" and "we can't say it categorically yet", but added: "That's what it feels like to me right now."
Comment: Create an intervention that doesn't solve the problem it is designed to solve. Then make it dependent on data that is independent of the intervention and subject to manipulation. Result: the nonsense intervention gets repeated over and over and over again. That's what it "feels like", no?
Under the government's roadmap for easing COVID-19 restrictions, 21 June is the date on which all legal limits on social contact are set to be removed.
But there have been suggestions that some separate measures - like mask wearing - could continue beyond that point.
Comment: Of course the will...
The government's roadmap for relaxing coronavirus rules acknowledges that social distancing is "difficult and damaging for businesses and, as a result, it is important to return to as near to normal as quickly as possible".
It adds: "Ahead of Step 4 [21 June], as more is understood about the impact of vaccines on transmission and a far greater proportion of the population has been vaccinated, the government will complete a review of social distancing measures and other long-term measures that have been put in place to limit transmission.
"The results of the review will help inform decisions on the timing and circumstances under which rules on 1m+, face masks and other measures may be lifted."
The prime minister's roadmap for lifting lockdown restrictions applies to England, with the other UK nations drawing up their own guidelines.
Social distancing has been in place for more than a year because of the COVID pandemic.
The "one metre plus" rule, introduced last June when it was reduced from two metres, means members of the public can be one metre away from each other as long as other measures are put in place to limit the transmission of the virus.
If these are not possible then members of the public should be two metres away.
Possible mitigations include wearing a face covering, installing screens, making sure people face away from each other and providing extra handwashing facilities.
Reacting to the PM's comments, Emma McClarkin, chief executive of the British Beer and Pub Association, said they "give our sector hope of a return to normality and viability".
"Given pubs are financially unviable under the current restrictions they face, being able to reopen without any restrictions at all from June 21st is going to be vital to their survival," she said.
Mr Johnson also spoke about the next scheduled easing of restrictions on 17 May.
On this date, a raft of businesses and premises will be able to reopen indoors, while international leisure travel also looks set to resume under a risk-based traffic light system.
The PM said he did not want to see an "influx of disease" once international travel gets going again, stressing the government was being "as cautious as we can" with its roadmap.
Asked if people should be planning a holiday abroad in the weeks and months to come, Mr Johnson said: "We will be saying more as soon as we can.
"I think that there will be some openings up on the 17th, but we have got to be cautious and we have got to be sensible and we have got to make sure that we don't see the virus coming back in."
A cross-party group of MPs has warned the government that limits on international leisure travel should continue even after 17 May.
The All-Party Parliamentary Group (APPG) on coronavirus has urged ministers to "discourage all international leisure travel" this year to protect the UK from COVID variants.
Speaking during a campaign visit to Lewisham in southeast London, Labour leader Sir Keir Starmer said: "We need to be very careful. I think it's clear that the virus is increasing in some countries around the world, so we have to be very, very careful.
"What we can't have is a repeat of last summer, where the lists were chopping and changing on a daily or even weekly basis.
"So I'll wait and see what the government has to say but I think we have to be very careful and very cautious."
I haven't been doing any.
Even though I've been probably been intermingling with vaxxed potential toxic time-bombs.