Despite a recent government plea, some councils have said further measures are needed before their refuse sites can reopen.
Local Government Secretary Robert Jenrick told the Commons that he expected local tips to reopen within weeks, but an increasing number of councils have said that this can only happen if their guaranteed sufficient staffing, proper protective equipment for workers and assistance from police forces - something that, at present, is lacking.
Many authorities have also said they will require visitors to provide proof of address before being given access to waste sites, to stop people travelling outside of their area and overwhelming services.
Since lockdown measures have been issued, some local areas have witnessed and reported a rise in flytipping incidents. Fly-tipping remains punishable by a fine of up to £50,000 or 12 months imprisonment.
Jenrick said: "With more people at home, more rubbish and recycling is being created. With many councils deciding to close their waste and recycling centres during the pandemic, there is also nowhere to take the extra rubbish. That is why we are asking councils to reopen these sites as a priority."