A&E units could partially close in the next few weeks due to the unprecedented four-day strike by junior doctors over pay.
The British Medical Association said on Wednesday it had started dialogue with mediators Acas.
But the Tories still refused to join talks unless the union abandons its demand of 35% “pay restoration”.
Labour leader Keir Starmer said he does not think 35% is affordable but called on Health Secretary Steve Barclay to “sort this issue out”.
The Royal College of Emergency Medicine said under-staffed A&E departments could decide to treat only patients arriving by ambulance.
Dr Adrian Boyle, president of the RCEM, said: “Most A&E departments will cope but it will be very tight.
“There are 40% to 60% of the usual medical staff working. It has been harder to arrange cover for this strike. Consultants are human like everyone else; they have families and childcare responsibilities.
“If A&E departments are not coping they will end up closing parts of the services.”
Dr Boyle said he was particularly worried the NHS would struggle to cope during the “hangover period” from the strikes next week.
Prof Philip Banfield, BMA council chair, said: “Restoring junior doctors’ pay should not be an unworkable proposition for talks and, through the services of Acas, we’re offering the Government an opportunity to discuss how we get there. We urge the Health Secretary to show the same willingness that we have.”
But Mr Barclay said: “I hoped to begin meaningful negotiations when I met the BMA last month.
“But its demand for a 35% pay rise is unreasonable. If the BMA move significantly on this and cancels strikes we can resume talks.”
