Whips are said to have warned Mr Johnson that more than 90 of his MPs, including several ministers, have raised serious concerns.
The reforms were thrown into sharp relief by the Tories’ shock defeat at the Chesham and Amersham by-election in June, in which the Lib Dems campaigned aggressively on planning.
A Government source said ministers would be in ‘listening mode’ on the issue when Parliament returns in September, adding: ‘We’ll listen and we’ll move.
‘We can take some of the edges off that are upsetting people and still get some important changes through.
‘The bottom line is we have got to get more houses built. The average age of a first-time buyer is 34. We have to get that down and give younger people a chance to get a stake in society.’
Tory rebels welcomed the softening of tone, but warned major changes would be needed to guarantee the passage of the Planning Bill this autumn.