Now confirmed:
We now have confirmation that a fifth Downing Street adviser resigned on Friday morning.
Elena Narozanski had been a member of the policy unit in No 10 and loyal to head of policy Munira Mirza, who quit yesterday.
https://www.bbc.co.uk/news/live/uk-politics-60256680
Conservative MPs can trigger a leadership contest if 15% of them 54 on current numbers in parliament write a confidential letter of no confidence in the prime minister to Graham Brady, chair of the 1922 Committee, the parliamentary group of the Conservative party in the House of Commons. Only he knows the exact number of letters that have been submitted.
Once the threshold is reached, there is a vote of confidence in the party leader, involving all Conservative MPs. If the prime minister wins a majority in this case 180 votes he would remain in office, and no new no-confidence vote could be triggered for at least 12 months. If he loses, or choses to resign, then a leadership contest takes place.
In a leadership election, Conservative MPs choose one candidate from those standing in a secret ballot. In the first round, any candidate who wins the support of fewer than 5% of MPs is eliminated. In the second round anybody winning less than 10% of the vote is eliminated. In subsequent rounds the bottom placed contender drops out until there are only two contenders left.
The choice of those two is then put to a postal ballot of Conservative party members around the country. The winner of that vote becomes the prime minister, with no obligation to call a general election to secure their position.
https://www.theguardian.com/politics/2022/jan/26/tory-mps-poised-to-send-letters-of-no-confidence-in-pm-after-partygate-report
That means that those sending in a letter have to be pretty confident they can get a majority of Tory MPs to sack him, or he's safe for another year. This may well mean he'll hang on by his fingertips either until the full Gray report comes out (or he admits he's been fined by the police for illegal gatherings during lockdown), or until the local elections have happened in May, in which a bad Tory result should convince even the unthinking loyalists that he's a ball and chain on their electoral prospects.