Outgoing Prime Minister John Key and several other senior ministers have endorsed English, but English said he was not taking a win for granted.
Bennett has been tipped as a possible deputy for English. Neither she nor English would discuss the issue yesterday.
Coleman, in a thinly-veiled shot at English, said there was a "significant appetite" for a "change from the status quo".
In a clear bid to paint himself as the fresh face compared to English, he said he was "relatively young" and although he had been politics for 11 years he was not a "professional politician". There are just four years between English and Coleman.
Coleman would not name a deputy, but spoke warmly about Adams. Adams said she was not attached to any ticket at this point.
Collins is the outsider in the contest. Declaring her bid yesterday, she said National could expect its "toughest challenge ever" at the 2017 election and she was the toughest candidate.
She also underlined her credentials as a woman, saying National had been led by men "for quite some time" and the party needed someone who could appeal to both men and women and all ethnicities. "I believe I can do that," she told reporters.
Her bid immediately raised questions about her controversial past, which has included a conflict of interest scandal involving her husband and allegations she tried to undermine a senior public servant.
An inquiry into the second case found she no evidence of wrong-doing, though she went further yesterday and said she had been "completely exonerated".