In a letter to the new prime minister, BMA chair Dr Chaand Nagpaul warned that the NHS has 10,000 unfilled medical vacancies - and that the gap is growing 'as a result of current government taxation policy'.
The BMA chair said the association was 'alarmed at the prospect of a no-deal Brexit', following Mr Johnson's pledge in his first speech as prime minister that the UK would leave the EU on 31 October 2019 'no ifs, no buts'.
Dr Nagpaul warned that a no-deal departure from the EU could have 'potentially catastrophic consequences across the NHS' - and repeated calls for a second public vote on Brexit.
He added that the prime minister's pledge to 'drastically reduce' GP waiting times would require 'action both to address the GP workforce crisis and the inadequate infrastructure of support in the community, which is currently impacting on primary care'.
The government is consulting on ways to offer greater flexibility to doctors in the NHS pension scheme, and has proposed a '50:50' option that would allow doctors to halve the rate at which their pension builds up by halving their contributions. But the BMA has warned that the measure 'will fail' - and has called for more radical changes.
In the letter to Mr Johnson, the BMA chair said: 'During the leadership campaign, the BMA welcomed your commitment to "fix" the lifetime allowance – but we also pointed out that the problems doctors face are further exacerbated by the annual allowance and tapered annual allowance.
'Without action by the Treasury to address the cumulative impact of these policies, doctors will have no choice but to reduce the amount of work they do for the NHS, or leave it entirely, to avoid unexpected tax bills that can be four, five, or even six figures in some cases.'
Dr Nagpaul warned the prime minister that the NHS 'simply cannot afford to lose' more staff. He wrote: 'We currently face the reality of severe all-year pressures in the NHS, in which waiting times are now routinely breaching the NHS constitution’s promise to the population. This is impacting adversely on doctors who cannot achieve the impossible.'
He said BMA polling showed that nine in 10 doctors fear 'making a medical error due to working in an environment plagued by systemic pressures and lack of capacity'.
The BMA chair warned: 'This is bad for doctors and patients alike – we need a valued NHS workforce in which everyone feels part of a properly resourced team, with the right mix of skills and tools to do the job properly and with fair reward.'
The BMA letter comes just days after the RCGP wrote to Mr Johnson. College chair Professor Helen Stokes-Lampard also urged the prime minister to rule out a no-deal Brexit. She called on his government to deliver on promises to increase the GP workforce.