Dr Chaand Nagpaul told the BMA annual representative meeting in Harrogate that in primary care, demand has 'far outstripped our impoverished capacity'.
The comprehensive service UK GPs provide should be a cause for celebration, he told the conference.
But instead general practice has been 'systematically devalued, attacked and defunded', with a real-terms reduction of £450m in funding over the past three years despite a 40m increase in patient contacts per year over the past five years.
Dr Nagpaul warned: 'GPs are struggling to square an impossible circle to manage the multiple complex physical and mental health needs of patients in the bare bones of a 10-minute consultation - an insensitive insult to so many of our most ill patients.
'We’re forced into providing conveyor belt care at breakneck speed, up to 60 times in a day, added to by an open-ended volume of phone calls, home visits, repeat prescriptions, results, reports and hospital correspondence. This is unmanageable, exhausting and unsustainable and puts safety and quality at risk.
'These intolerable pressures have butchered the joy and ability of GPs to care for their patients, leading younger doctors to shun general practice in favour of a career in hospital.'
The GPC chairman warned that ministers 'ignore this workforce crisis at their peril, which seriously risks leaving patients bereft of a GP service in some areas'.
A DH spokeswoman said: 'It is scaremongering to say that GP services are "imploding". The number of GPs has gone up by 1,000 since 2010 and we’ve taken tough decisions to protect the NHS budget so we can strengthen family doctoring, reform out of hospital care and improve GP access for 7.5 million people.
'GPs agreed to be at the heart of our radical plans for more personalised community care in return for cutting their targets by more than a third to free up more time with patients.'