The leading Conservative candidate to succeed David Cameron as prime minister has pledged to unify her divided party and country behind a negotiated British exit from the European Union.

Home Secretary Theresa May, who holds a strong lead over four party rivals ahead of Tuesday's initial leadership ballot, says she can bridge the gulf between ardent opponents and supporters of EU membership.

May officially supported Cameron's pro-EU efforts but avoided campaigning herself. She argued Sunday this relative neutrality would help her build consensus between the 17 million who voted for a British exit, or "Brexit," and the 16 million who voted to remain in the June 23 referendum.

May said: "I've been clear that Brexit means Brexit. What we need to do is to bring those two sides together."