Senior backbenchers urged Johnson to use the crisis to"reset"his Downing Street operation by appointing an experienced party figure who could build bridges with the parliamentary party.
Symonds led the revolt against Cain's promotion by making it known that she objected to him becoming the Prime Minister's right-hand man.
Her allies said she was"uncomfortable"with the appointment,questioning Cain's suitability for the role.
Stratton,who would have reported to Cain in his new job,is also understood to have objected,with both women expressing unhappiness about his at times abrasive manner and questioning the communications strategy under his leadership.
But on Wednesday night,London time,Cain said that"after careful consideration I have this evening resigned as No 10 director of communications and will leave the post at the end of the year".
He confirmed he had been offered the post of chief of staff,saying it had been an"honour"to have been asked to serve in the role. Johnson,meanwhile,described him as"a true ally and friend"who would be"much missed".
Cain will be replaced by James Slack,the Prime Minister's official spokesman,who has served both Johnson and Theresa May in the Civil Service post.
Johnson had approached Cain at the weekend to discuss his appointment as chief of staff,only for Symonds to raise objections,insiders said. A promotion for Cain would have ensured that Cummings's authority was not challenged by a new face in the Prime Minister's office. Instead Tory MPs were last night calling on Johnson to start afresh with his top team.
Sir Charles Walker,a vice-chairman of the 1922 Committee,said:"The PM has got to use this crisis to good use and get someone into 10 Downing Street who backbenchers know and respect,and will have the Prime Minister's and party's interests entirely at heart."
Senior Tories were last night urging Johnson to appoint David Canzini,a close ally of Sir Lynton Crosby who helped to run Johnson's leadership campaign,to the role. Cain's resignation will increase the influence of Symonds and Stratton,who only moved over to No10 last month after serving as the Chancellor's communications chief.
They were understood to be unhappy with the prospect of Johnson's top team,which also includes Simon Case,the Cabinet Secretary,being all-male.
Johnson was already under pressure from senior Tory MPs to appoint a party grandee to become his chief of staff. Sajid Javid,the former chancellor,had put himself forward,and others whose names have been linked include Oliver Dowden,the Culture Secretary,and the former Cabinet ministers Greg Clark and Sir Michael Fallon.
Cain is understood to have offered his resignation from his current role last week,complaining that if Stratton became the face of No 10 and a new chief of staff was appointed he would be squeezed out. Johnson then discussed with him the idea of a promotion.
One source who has been close to Johnson said that they suspected Symonds had identified her preferred candidate for the job,saying:"She won't be taking this quietly... She will have someone in mind."
However,allies of Cain defended his record and said he would have been the right choice. One said:"When Boris was in hospital and Dominic Cummings was laid up in Durham with coronavirus,Lee was left running the show. Not just communications,he was looking at every aspect of policy."
Cain worked for Johnson as his media adviser at the Foreign Office and stayed with him when he resigned over Theresa May's Brexit deal.
Stratton was not Cain's preferred candidate to hold No 10 press conferences when they become a daily event next year,and as chief of staff he would have been her boss. But Stratton is understood to have made it clear that she must have direct access to the Prime Minister to be able to do her job.
Cain and Symonds are understood to have fallen out when she posted photographs of herself sitting on a bench with Johnson on her Instagram account without telling him in June last year.