A survey by ConservativeHome found that 35% of members picked the former foreign secretary as their favourite to take the helm of the party next.
This marks an extension in Mr Johnson’s lead at the top of the table in the past four weeks. Last month 29% of those polled said he should be the next to head the party.
Home Secretary Sajid Javid was the second post popular candidate with 15%, and Jacob Rees Mogg came in third place with 10%.
ConservativeHome, the website for Tory grassroots activists, is considered to be a reliable guide to the opinions of party members.
Editor Paul Goodman wrote: ‘For the moment at least, committed Brexiteers are increasingly lining up behind Johnson, and Javid’s cause stands out among Party members who don’t want the ex-Foreign Secretary, and are searching for an energetic and capable Minister to back.’
The result comes a few days after Mr Johnson doubled down on his staunch criticism of Mrs May’s Chequers blueprint for Brexit.
In his weekly Daily Telegraph column he launched a searing attack on the PM’s plan, branding it a ‘fix’ that can only lead to victory for the EU and would leave the UK with ‘diddly squat’.
The Prime Minister responded with an uncharacteristically strong slapdown of her former cabinet minister, accusing him of having ‘no new ideas’.
Mrs May’s official spokesman said: “Boris Johnson resigned over Chequers.
“There’s no new ideas in this article to respond to. What we need now is serious leadership and a serious plan.”
Mr Johnson is rumoured to be considering a bid to oust Mrs May from Number 10, and has agreed to speak at a rally of party delegates on the eve of Theresa May’s Conservative Party conference speech.
The provocative move is widely viewed as part of an attempt to establish himself as a leadership candidate.
But despite his popularity amongst party members, Mr Johnson does not enjoy universal support within the ranks of his fellow Conservative MPs, making it difficult for him to make it onto the ballot.
How would a Conservative leadership contest work?
A leadership contest can be triggered in two ways. Either the leader must resign, or at least 15% of Conservative MPs need to write to the chairman of the 1922 Committee expressing a lack of confidence in the current leader.
The 1922 Committee is a committee of all the Conservative backbench MPs, which meets weekly while the House of Commons is sitting.
Any MP who wishes to run as candidate needs the support of two fellow MPs in order to get onto the ballot paper. If only one candidate is nominated, they automatically become the next leader.
Tory MPs then vote using the first past the post system. If more than three candidates have been nominated, the one with the lowest proportion of votes is eliminated and another ballot is held. This process continues until two candidates remain.
Conservative Party members then vote for the two nominees, and the winner becomes the new leader.