Concerns have been raised about the standards of staff training and medical education at Queen’s Hospital in Romford and King George Hospital in Goodmayes.
The General Medical Council (GMC) said standards were not being met following a visit to the hospitals run by the Barking, Havering and Redbridge University Hospitals NHS Trust (BHRUT) in April.
The GMC's concerns relate to the standards of delivery of medical education and training in acute internal medicine at BHRUT.
Doctors in acute internal medicine assess, investigate, diagnose and manage the care of patients with conditions that have developed quickly, show serious symptoms and may be life-threatening.
The GMC says 10 standards are not being met in this area at the hospitals in Romford and Goodmayes.
As a result, the speciality has been placed into an "enhanced monitoring process" by the GMC.
The standards not being met include making sure learners are able to meet with an education supervisor as frequently as required and ensuring the hospital has the capacity, resources and facilities to deliver "safe and relevant learning opportunities".
The GMC also raised concerns that doctors may be experiencing behaviour that undermines their professional confidence, performance or self-esteem.
In a formal notification to BHRUT, Professor Colin Melville said: "Failure to meet these standards and requirements may have an impact on patient safety and the quality of education."
Andy Walker, a Seven Kings resident who has been campaigning for more resources at hospitals in the boroughs since 2011, said corners are being cut in training in order to cope with demand at the hospitals.
Mr Walker said: "Senior doctors and junior doctors don't have time to train because they are too busy fighting the chaos that is in A&E during busy periods.
"They just can't cope with the lack of resources they have - it's no surprise that they cut corners on training to ensure that they meet government A&E benchmarks.
"It's an institution under strain. It just doesn't have the resources to deal with patients and train doctors at the same time.
"If you've got someone coming into A&E with pneumonia, but doctors have a training session planned, are you going to go to the training session or will you make sure that patient is treated within the first four hours? The training will be cancelled. Training comes second."
Chris Bown, interim chief executive at BHRUT, said: "Providing a supportive learning environment for our trainees is a responsibility we take very seriously so these findings are disappointing.
"We are committed to continuing to improve the culture within our trust, tackling the wider issues which we face.
"On the specific points raised here, we have already made good progress with improving our support by being clearer about rotas, trying to reduce the numbers of gaps, and improving the visibility and access to consultants, particularly at change overs.
"However, there's much more to be done. We will see this through, working with the GMC and our staff to improve."
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