The trust manages two areas of woodland in Peterborough - Orton Longueville and Stanground.
The call comes three years on from a devastating blaze that destroyed swathes of moorland and wildlife looked after by the charity – and as it warns there have already been nine fires on its sites this year.
The trust is launching a national “love your woods” campaign which aims to encourage people visiting its woodlands and moorlands to leave no trace and help the protection of its special sites.
It warns that barbecues and small fires on moorland and woodland can easily get out of control and rip through the countryside, damaging habitats and wildlife.
In the summer of 2018, which also saw drought, fire swept through the moorland at Smithills near Bolton, damaging a third of the 1,700 hectare site, killing around 2,000 trees, wiping out habitats and displacing rare birds such as curlew.
It took weeks for the fire service and the Woodland Trust to bring the fire under control and costs for the ongoing recovery are rising above £1 million, the charity said.
This year a fire at Cave Hill in Northern Ireland damaged a large area of the site, while at Castle Hills in Northumberland and Martinshaw in Leicestershire there have been a series of fires.
Al Crosby, the Woodland Trust’s regional director for northern England, said: “Our sites are a wonderful place to visit with so much diversity – from mountainous Ben Shieldaig in Scotland and the moorlands of Smithills, to community woods and lowland forests towards the south of England, and everything in between.
“We of course want people to enjoy them but also to take care of them, which is why we have launched this campaign, all about recognising what’s special about these places, and how visitors can show their love for them and help us to keep them that way.
“Our key message is to people – help us to protect the precious woods and wildlife near you – please don’t light fires, it poses untold risk to people and wildlife.
“Even if people think they are in control, one minute it can soon change and the affects can be absolutely catastrophic.”
At Smithills the charity is rewetting the moorland to keep it in a more moist condition to boost a healthy habitat and the growth of sphagnum moss, while birds such as curlew, snipe and golden plover have started to make a return.
The trust estimates it will take 10-15 years before the landscape will get back to how it was before the fire. It will continue to restore the site and plant more trees, it said.