Another poll suggests that the public back Jeremy Hunt to be the next prime minister over Boris Johnson.
Foreign secretary Hunt is the favoured successor to Theresa May among the public at large, by 41% to 29% for Johnson, according to the YouGov poll.
But the research puts Johnson ahead by 48% to 39% among Conservative voters, and it is the Tory party membership who will decide the victor.
The research suggests momentum is going in Hunt’s favour. He is up to 28% of the public believing he would be a good PM, compared with 43% thinking he would be bad.
Johnson is at 25% and 58% respectively, with the research suggesting he is going backwards with the public.
The research put Johnson ahead on handling Brexit, but behind on honesty and good moral character.
The poll, which questioned people on Wednesday and Thursday, was published as the rivals face the membership in a series of hustings across the country.
YouGov director of political and social research Anthony Wells wrote: “If the Conservatives are looking towards Boris Johnson as a magic election winner, the evidence is simply no longer there.
“A decade ago he had a reputation as the Tory who could reach voters other Tories could not, and significantly outperformed his party in the 2012 mayoral election.
“However, our latest polling does not suggest he offers any innate electoral advantage over Jeremy Hunt.”