Hilton said it had taken the council “time to get everything legally right so we could go in there without any challenge and secure the site”.
About 75 tonnes of waste had been removed from the site before asbestos was found, he said.
“What’s been coming in is not in the car boot or something like that, it’s lorries coming in and [the land is] being accessed through Severnside Farm,” Hilton said.
“It’s been dumped on somebody else’s land and they’ve been powerless to stop it.”
In his letter, Hilton also requested support from national agencies, including the National Crime Agency, to help identify and prosecute those behind the waste dumping.
Speaking on behalf of the government, a spokesperson for the Environment Agency said: “We know how much damage illegal waste sites have on communities.
“We have used a consistent set of criteria to identify the highest-risk sites right now, but that doesn’t mean everywhere else is being ignored.
“Cleaning up sites is just one part of the system change, as we are strengthening our intelligence and analysis capability to tackle waste crime with stronger enforcement powers and more officers on the frontline.”