Nominations to become David Cameron's successor as Conservative leader and UK prime minister should open this Wednesday (29 June) and close at noon on Thursday, an influential group of Tory MPs have proposed.

The executive of the 1922 Committee, which is made up of the party's backbench MPs and chaired by Brexit backer Graham Brady, also advised electing a new leader by 2 September.

The move comes after Cameron announced his intention to resign as prime minister and Conservative leader in the wake of the UK's decision to vote to split from the EU in a 23 June referendum.

Cameron, who was elected to the top of the Conservative Party in December 2005, had advised electing his successor by October.

Former Mayor of London Boris Johnson, chief spokesman of the successful Vote Leave campaign, is expected to run in the race as is Home Secretary Theresa May.

Brexit backers Andrea Leadsom, a former city minister, and Dr Liam Fox, a former defence secretary, have so far failed to rule out putting their names in the hat. Remain campaigner Nicky Morgan, the education secretary, has also hinted at running.

The 330 Conservative MPs, like the party's 2005 leadership election, will vote until two contenders are left, and the candidates will go head-to-head in a vote decided by the party's membership.

Conservative Party leadership election rules

1. The Leader shall be elected by the Party Members and Scottish Party Members.

2. A Leader resigning from the Leadership of the Party is not eligible for re-nomination in the consequent Leadership election.

3. Upon the initiation of an election for the Leader, it shall be the duty of the 1922 Committee to present to the Party, as soon as reasonably practicable, a choice of candidates for election as Leader. The rules for deciding the procedure by which the 1922 Committee selects candidates for submission for election shall be determined by the Executive Committee of the 1922 Committee after consultation of the Board.

4. If there is only one candidate at the time laid down for the close of nominations, that candidate shall be declared Leader of the Party.

5. Only those Party Members and Scottish Party Members who were members of the Party from the time of the call for nominations by the Chairman of the 1922 Committee for the election of the Leader and have been members for at least three months immediately prior to the close of the ballot for the election of the Leader shall be entitled to vote.

6. A candidate achieving more than 50% of the vote among the Party Membership shall be declared elected Leader of the Party.

7. In the event of there being only one valid nomination at the close of nominations prior to the first ballot being held by the Parliamentary Party for the election of the new Leader, the election of the nominee may if so ordered by the Board be ratified by a ballot of the Party Members and Scottish Party Members to be held within one month of the close of nomination.

8. Subject to the provisions of this Constitution, the rules for the conduct of the ballot or ballots of Party Members and Scottish Party Members shall be agreed by the Board and the Executive Committee of the 1922 Committee.

9. The Chairman of the 1922 Committee, acting on behalf of the Party, shall act as Returning Officer for all stages of the election.