Earlier this month, the Guardian newspaper reported that Allan was facing claims of inappropriate behaviour from four women.
One of the allegations relates to Allan's conduct at supermarket group Tesco, which he has chaired since 2015, and three to his time at business lobby group the Confederation of British Industry (CBI), where he was president from 2018 to 2020.
Three of these allegations are vigorously denied by Allan, and for the other Allan unreservedly apologised for a comment he made.
In a statement on Tuesday, Allan said he regretted having to step down.
"My early departure from Barratt is a result of the anonymous and unsubstantiated allegations made against me, as reported in the Guardian which I vehemently deny."
Tesco said on Friday that Allan would not seek re-election as a director and would step down as chairman at its annual shareholders' meeting on June 16.
Barratt said on Tuesday that Allan would step down as its chair on June 30, earlier than his planned retirement on Sept. 6 after nine years in the role. He will be succeeded by Caroline Silver.
"The board believes it is in the best interests of Barratt to accelerate the planned transition to the new Chair of the Board to prevent the ongoing impact of the allegations against John from becoming disruptive to the Company," Barratt said.
It added that it has not received any complaints about Allan during his tenure at the company.
(Reporting by James Davey in London and Aby Jose Koilparambil in Bengaluru; Editing by Sherry Jacob-Phillips and Louise Heavens)
