The ECB also released a statement regarding the amateur game in the UK.
But that isn't a threat to the next month's England-West Indies Test series, for that is elite-level game and will be played in a bio-secure bubble from July 8.
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Johnson, responding to a question from Conservative MP Greg Clark in the House of Commons, said it was too soon to lift current restrictions imposed to prevent the return of the amateur game.
"The problem with cricket as everybody understands (is) that the ball is a natural vector of disease, potentially at any rate. We've been (a)round it many times with our scientific friends," he was quoted as saying.
"At the moment, we're still working on ways to make cricket more COVID-secure but we can't change the guidance yet."
The news that relaxations won't be implemented on recreational cricket is a serious blow to England's non-professional clubs.
The ECB, on its part, said it will continue working closely with the government in hope to resume the recreational game at the earliest, possibly "on or around July 4".
"The England and Wales Cricket Board (ECB) along with the nation’s cricket players are keen to see the imminent and safe return of our sport at recreational level and have been working hard with government to achieve this," the board said in a statement.
"We believe that cricket is a non-contact sport, with very low risks of exposure, and that it can be played as safely as many other activities being currently permitted. It is our strong desire to work with the government to see the return of recreational cricket on or around July 4, as they continue to lift other restrictions more broadly across society."
"We are heartened that the government has already permitted the return of other ball sports, including tennis and basketball, and we are sure that our interpretation of the risks around ball transmission is consistent with these other games," it added.
"We can confirm that any guidance we share with the game will include directions on how to mitigate any risk from handling the ball as we continue to prioritise the health and safety of the cricket family in all our decision-making."
(Inputs from PTI)