Conservative Party members do not strongly support any cabinet ministers to succeed Theresa May, with most saying “none of the above” when asked who should be the next leader in a new survey.

More than a third ignored those considered to be the front-runners for the top job, with only Brexit Secretary David Davis scoring more than 10 per cent support.

One Conservative frontbencher told The Independent the result showed it is now time for the party to look beyond the current crop of cabinet members to the lower rung ministers for the next leader.

The ConservativeHome website’s monthly survey of party members showed the largest proportion, 34 per cent, of the more than 1,200 people surveyed, said they did not back any of the names given to them for next leader.

Mr Davis’s support fell just short of 20 per cent, Boris Johnson won 9 per cent and Dominic Raab, not a member of the Cabinet, took almost 8 per cent.

Chancellor Philip Hammond, who has been leading a drive to nuance the Government’s approach to Brexit took 5 per cent, while International Development Secretary Priti Patel and Home Secretary Amber Rudd took about the same.

A minister said: “Theresa will be around until 2019. After that how we move to the next person is just a matter of choreography – who will it be, how will it happen and how long will it take?

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“The people who are there just aren’t inspiring, and because it’s going to be a while until the next contest, it means others have a chance to start building a reputation and making a name.”

More junior ministers in the frame are Damian Hinds, Mr Raab, Rory Stewart and potentially Jo Johnson, Boris’s younger brother.