Local people claim they have already seen a plume coming from a new plant.
Einar Thronsen was among those who helped hide four British air crew in 1944, says his grandson.
Household rubbish will be sent to the Rivenhall facility instead of going to Essex landfill sites.
The first truckloads of waste were delivered to the Rivenhall Incinerator on 21 July, the site says.
A waste firm is accused of breaking planning rules by not building recycling facilities at the site.
The historical tree lies on a proposed route for 50m-high (164ft) pylons.
They flew missions behind enemy lines, dropping agents and supplies, says a historian.
Some of the men who were there look back nearly 80 years to the largest single airborne operation.
Crews from Essex and Suffolk are recognised for their roles in the liberation of the Netherlands.
