The move would ease pressure on the capital’s public transport network and encourage more workers back to sites.
One trade contractor said: “I was at a large site in central London this morning and many workers refuse to travel by tube because of the risk to health.
“Some operatives are taking in their vehicles and risking getting a ticket.
“There were cars and vans parked on single yellow lines all around the site and I was told it’s OK to park and ‘don’t worry you won’t get a ticket’.
“I was told the same thing last week at a different site but I’ve paid too many fines over the years to take any risks.
“The phone parking system is still in operation and taking money for parking. Why can’t the councils take a stance on this and stop all phone parking bays from taking money off workers who are still going to work?
“The streets of London are eerily empty and there are plenty of places to park if only they’d do the sensible thing and stop all parking tickets.
“The additional parking will not cause congestion as the streets are so empty.”
A London Councils spokesperson said: “In this difficult time boroughs are adopting pragmatic approaches towards parking enforcement, with priority support given to key workers such as NHS and social care staff.
“Parking flexibilities have been introduced across London for key workers in emergency, care, and transport services because their roles are crucial to supporting the capital’s response to Covid-19.
“It should be noted that parking restriction policies are decided by individual local authorities. Constructions workers should check with the relevant borough to clarify local arrangements.”
Transport for London suspended the congestion charge across the capital on March 23.