A letter to the Times that supported reforming rather than scrapping the new online recruitment system aroused further anger among junior doctors.
Doctors have been calling for the Medical Training Application Service to be ditched after widespread dissatisfaction at the poorly designed recruitment forms and processes and security breaches.
Last week health secretary Patricia Hewitt backtracked on her defence of the system, saying that after the first round of recruitment interviews it would only fulfil a monitoring role this year.
The BMA was reportedly bombarded with complaints about Johnson’s letter, which many felt did not adequately reflect members’ frustrations.
Johnson told Channel 4 News: “I am having to resign because I have lost the confidence of a very large number of members of the BMA council.
“But this is no ordinary political situation. The medical profession is on the edge.”
Hewitt also faces calls for her resignation from medics and opposition politicians.