Lewisham and Greenwich NHS Trust has been told it needs to improve patient care for the third time in three years.
An inspection by the Care Quality Commission (CQC) has again identified numerous failings in patient care.
The CQC carried out an inspection in June 2016 and again in March 2017 after it received an increased number of complaints from patients.
In 2014, CQC inspectors also found the trust "requires improvement". The trust said it had improved since March.
Lewisham and Greenwich NHS Trust serves a population of half a million people across the London boroughs of Lewisham, Bexley and Greenwich.
Following the latest inspection of Queen Elizabeth Hospital in Woolwich in March, the CQC again said the trust required improvement.
"We have noted that the pace of, and extent of change since our inspection of 2014 has been slower than anticipated," the report stated.
In the most recent report, inspectors raised concerns over:
- Patients with tuberculosis not being properly isolated
- Staff seen not routinely sanitising their hands between dealing with patients and on entering and leaving wards
- Anaesthetists and surgeons taking outdoor bags and briefcases into anaesthetic rooms and theatres on three occasions, posing a risk of infection
- Poor standards of cleanliness - both of the environment and of the equipment - in maternity and gynaecology wards where green 'I am clean' stickers had been used, indicating equipment had been cleaned that day
- Inadequate provision of end of life care across the organisation
CQC's chief inspector of hospitals, Professor Ted Baker, said: "The trust has not made sufficient progress since our last comprehensive inspection.
"There remain areas of unresolved risks and areas for significant improvement."
'Proud of staff'
Dr Elizabeth Aitken, medical director for Lewisham and Greenwich NHS Trust, apologised to individual patients and their families for failures.
But she added the trust had launched "a major safety and quality improvement plan immediately after the CQC inspection in March" and "had made significant improvements for patients".
"The CQC report also acknowledged several areas of good and outstanding practice and highlights many areas where Lewisham and Greenwich NHS Trust has improved since the last Trust-wide inspection in 2014.
"We are extremely proud of our staff who work so hard, often under significant pressures," she said.
The CQC report also showed 17% of jobs available at the trust - a total of 1,159 roles, including 346 nursing and midwifery roles - were vacant.
The average vacancy rate in south London hospital trusts was 15% at the end of 2015, according to the Royal College of Nursing.
In north, central and east London, 18% of jobs available at NHS trusts were vacant in May.