Mr Clarke, who devised part of the Tory strategy to win the election, has denied any role in the episode.
Mr Halfon, who is not married but has a long-term partner, said: “What I did was wrong, and I feel ashamed. I am not proud of myself. The most important thing to me is to continue to repair my relationship with my partner."
The Harlow MP was promoted to the cabinet and given the key role at the top of the party by David Cameron following the general election in May.
He has enjoyed a rapid rise through the Tory ranks, due largely to his reputation as a campaigner for consumer rights.
Widely hailed for his lower petrol price crusade, he was appointed as Chancellor George Osborne’s private secretary last year.
