The race to replace Theresa May has come down to the final contenders, with Hunt and Johnson taking part in nationwide hustings before the party votes.
In a YouGov poll of public opinion, Hunt now leads Boris as the public's preferred successor by 41 percent to 29 percent.
However, the vote will be decided by Tory party members alone.
Among Conservatives, Johnson is ahead by 48 percent to 39 percent.
The survey showed a quarter - 25 percent - of people think Boris Johnson would be a good Prime Minister.
But 58 percent said the opposite of Mr Johnson leadership (a net figure of -33, compared to -18 a fortnight ago).
Meanwhile, 28 percent believe Hunt would make a good Prime Minister.
And it seems the public are more confident of Mr Johnson’s vision of Brexit, with 22 percent of people thinking Mr Johnson would lead Britain out of the EU, compared to Hunt with 12 percent.
Another 43 percent think be bad (a net figure of -14, compared to -24 a fortnight ago).
Meanwhile, the foreign secretary told a hustings in Exeter he would love Mr Johnson on board as he was an "enormous talent".
But Johnson denied making the same off to Hunt if he became the next Prime Minister.
Around 160,000 Conservative members will begin voting next week with the new leader named on July 22.