Householders are being urged not to rush to the dumps when they reopen, amid concerns over long queues of people trying to get rid of lockdown rubbish.
Many household waste and recycling centres are closed during the lockdown because they could not be operated within social distancing rules and to allow councils to focus on household waste collections.
The Government has since said it wants to see councils reopen tips, with social distancing in place, while residents should only go if their journey is essential.
Closure of tips and curbs on some waste collections, along with more waste being generated by people embarking on spring clean clear-outs, DIY projects and gardening, has raised concerns over an increase in fly-tipping.
Greater Manchester is one of the areas where tips have reopened, with a system alternating the days vehicles are allowed to attend depending on whether their car number plate ends in an even or odd number.
Long queues have been reported and across the country residents are being urged by councils to avoid rushing to the tip when they begin to reopen – and instead to "reduce, reuse and recycle" their rubbish wherever possible.
The District Councils' Network and County Councils' Network have issued the warning as they fear a surge in demand.
As centres are expected to gradually reopen over the next few weeks, not everyone will be able to dump their rubbish if there are high numbers of people queuing to get in, the council bodies warn.
They say nearly all councils have reported higher than usual levels of waste in recent weeks, but about nine out of 10 (89%) are continuing to operate normal "black bag" collections, with the remainder seeing only minor disruptions.
Four-fifths of recycling collections continue to operate as normal and two-thirds of food waste collections are going ahead at they would normally do.
But less than a third of councils are operating a normal bulky waste collection.
Many councils have seen reductions to their waste teams, as staff self-isolate and collections are disrupted by the need for social distancing.
Dan Humphreys, from the District Councils' Network, said: "We appreciate how hard people have been working to keep on top of waste but we would like to stress that it won't be possible for everyone to suddenly get rid of any rubbish they have built up over recent weeks all in one go."
Sam Corcoran, communities and environment spokesman for the County Councils Network, said: "We would encourage residents to only take a trip to their recycling centre if absolutely necessary, reusing or recycling items using kerbside collections wherever possible."
An Environment Department (Defra) spokesperson said: "During this challenging time, people should only visit a waste and recycling centre if the journey is essential, in accordance to the latest social-distancing guidelines.
"We are working closely with local authorities and the waste industry to see how we can re-open these sites in the coming weeks, to make sure waste collections are prioritised appropriately and that all parts of the waste system continue to run as smoothly as possible.
"Local authorities should maintain black bag collections and prevent waste from building up to protect the environment and public health."