In Newham, where just 35 percent of the population has received both jabs, anyone entering, or working in, a council building will have to wash their hands, wear a mask and maintain social distancing.
Mayor Rokhsana Fiaz said: “It is the right thing to do for everyone to continue wear masks as they do now in order to keep each other safe.
“With only 35 percent of people fully vaccinated, Newham people are at serious risk from the coming third wave.
“I am fighting hard to make sure Newham gets its fair share of vaccinations but until everyone is fully vaccinated we must keep each other safe by continuing to wear masks as before.”
In Hammersmith and Fulham only 36 percent of residents are fully vaccinated. Council leader Stephen Cowen told the Standard mask wearing would be enforced in public buildings.
“We think it’s essential and are asking the public, local retailers and local hospitality businesses to keep policing mask wearing,” he said.
“Keep wearing masks in all enclosed public spaces and crowded spaces outdoors and maintain social distancing.”
Barking and Dagenham leader Darren Rodwell said staff who can work from home would continue to do so and masks would have to be worn in council buildings until at least September.
Some 42 percent of residents have been double jabbed in the borough.
“The fact is [Covid] cases are going up,” Mr Rodwell said.
“The rules won’t change here until September at the earliest. It is unfortunate that people are being told it is all fine now.”
Brent council, where 41 percent of residents are fully vaccinated, said it would also be asking anyone entering public buildings to wear face masks.
In Tower Hamlets just 31 percent have been double jabbed - the lowest number in London.
Mayor John Biggs said: “Wearing face coverings in crowded places, council buildings and on public transport will help us do that and give people the confidence they need to go about their daily lives.
“While national restrictions are being lifted, I think the government should be encouraging people to continue to wear masks. It’s important to recognise we still have a duty to one another and wearing a mask in certain situations will continue to keep our community safe.”
The government has announced that most of England’s legal Covid restrictions will end on Monday.
Transport Salaried Staffs Association general secretary Manuel Cortes echoed the sentiments and said he hoped “other transport authorities and rail operators will take similar measures to protect both staff and passengers”.