Conservative Party lawmaker Chris Skidmore submitted a letter of no confidence in Prime Minister Boris Johnson on Wednesday, as the British leader faces intensifying calls to quit.

Skidmore's move comes one day after a number of ministers in Johnson's government resigned over a series of scandals that have blighted the current administration.

While Johnson narrowly survived a confidence vote last month, giving him 12 months of immunity from another one, some lawmakers in his Conservative Party have been trying to change the party rules to shorten that immunity period. 

Elections for the membership of the so-called 1922 Committee, which sets the rules, are due to be held shortly.

"It is vital therefore that the 1922 must urgently reconsider the rules that prevent a new vote of no confidence from taking place," Skidmore said.

Other lawmakers had appealed to Johnson's top team of cabinet ministers to move against him, but aside from finance and health secretaries who quit on Tuesday, media reports suggest other senior members of the cabinet, including Foreign Secretary Liz Truss, Defence Secretary Ben Wallace, and Levelling Up Secretary Michael Gove are staying in place.

The prime minister has shown no signs of being willing to step down.

(With input from Reuters)