Calls are being made for an independent investigation into threatening messages sent by Gavin Williamson to the then-Tory chief whip.
The caller claimed the UK's predominantly white electorate "want to see a prime minister who reflects them".
It comes amid bitter divisions in the parliamentary Tory party about its future direction.
The new prime minister will take office next week.
Bookies are also placing bets on how long Liz Truss has left in office as the UK faces economic chaos.
The chancellor performed a massive U-turn on Monday by ditching plans to scrap the 45p tax rate.
The new PM is less popular than her predecessors when they started, new polling suggests.
These are the things Britons want to know about the favourite in the Conservative Party leadership contest.
Rishi Sunak backer Simon Hart said Truss should be 'really nervous' about her team allegedly saying the contest is in 'in the bag'.
Macron said France remains friends with the UK 'in spite of its leaders'.
Tory leadership frontrunner Truss said she would immediately reverse Sunak's National Insurance rise at an emergency budget.
The ex-chancellor told the Sunday Times 'you must be joking' when asked if he would quit his rural seat if he doesn't become prime minister.
One government minister said Sunak's remarks were among the 'weirdest - and dumbest - things I’ve ever heard from a politician'.
For the second time in three years, a tiny segment of the UK population will be electing the next prime minister.
'For people who suddenly care about the environment, that was an important part of her agenda. She was the first person to reintroduce beavers.'
Truss, the Conservative leadership frontrunner, made the pledge despite the Rwanda policy being in legal limbo.
The five remaining contenders in the race to be prime minister face a series of votes this coming week.
None of the Tory leadership hopefuls raised their hand when asked in the second TV debate if they would have Boris Johnson in their cabinet.
There will be three televised Conservative Party leadership debates, it has been announced.
'I have friends who are upper class, I have friends who are working class… well, not working class.'
'I don’t think it’s naive.'
Grant Shapps was one of Boris Johnson's most loyal ministers.
Conservative and Labour MPs are engaged in a blame game over this week's rail strikes.
The prize of sitting around a table for a meal with the last three British prime ministers was auctioned at the controversial Conservative Party summer fundraising ball on Monday night.
Tuesday's front pages were all devoted to the prime minister's future after he survived a confidence vote among his own MPs.