Among the requests agreed was a doctor to work at Nottingham City Hospital’s neonatal intensive care unit over the weekend.
Three BMA members were also brought in to work a night shift at the Northern General in Sheffield.
But the BMA rejected a request by Milton Keynes Hospital for a doctor to carry out prostate cancer checks. In that case the BBC understands a doctor did return to work under their own volition.
A BMA spokesman added: “It remains our position that this agreement will be available for the NHS to rely upon should a safety-critical, urgent event occur.
“That process is there day and night throughout industrial action, and we remain ready to respond to any emergency requests.
“However, we need to be clear that the purpose of this agreement is not to facilitate the continued delivery of non-urgent care at the same time as senior doctors are covering for residents taking industrial action, as trusts simply do not have enough senior doctors to do that safely.”
NHS England sources said it was particularly disappointed with the rejections as the national organisation was now vetting every request from hospitals to ensure a consistency in approach between different places.
Every request, they said, was based on “rigorous assessment”.
“We absolutely recognise the legal right for people to strike, but we also recognise that it’s essential to maintain as many services for patients as possible,” they added.
The five-day strike by resident doctors is due to run until 07:00 BST on Wednesday.