At the same time, 50% of conservatives oppose Johnson's appointment to the new cabinet.
Moreover, 55% of those supporting Foreign Secretary Liz Truss's bid for the leadership said that Johnson should be in the next cabinet, with only 18% of those backing former Treasury Secretary Rishi Sunak saying the same.
The poll results showed that Johnson only outmatched former UK Health Secretary Jeremy Hunt (31%), who had been eliminated from the Tory leadership race in the first round.
Former Minister of State for Equalities Kemi Badenoch is leading the list of British politicians who should be given a cabinet role with 84% of the votes. UK Defense Secretary Ben Wallace (81%) and Attorney General for England and Wales Suella Braverman (66%) are holding second and third places.
Both State Minister for Trade Policy Penny Mordaunt and Chair of the Foreign Affairs Select Committee Tom Tugendhat, who had also lost in the earlier stages of the Tory leadership race, gained 63% of the votes.
The new YouGov survey was conducted among 730 Conservative Party members on July 20-21.
Truss and Sunak are the two final candidates in the election race for the post of prime minister and head of the Conservative Party, following Boris Johnson's resignation on July 7.
The last round will take place by mail from August 4, with the winner determined by all party members, of whom there are about 200,000 to date. The results are expected to be announced on September 5, when Parliament resumes its work after the summer break.