Marine life in the area is the most protected in Europe, they say, but legal protections are being ignored.
The campaign has been ongoing for years.
Waste dredged in Devonport Dockyard is deposited in Whitsand Bay near Rame Head in southeast Cornwall.
The practice, approved by the Marine Management Organisation, allows larger ships to access the harbour.
Phil Hutty, Liberal Democrat prospective parliamentary candidate for south east Cornwall, said: "We're very grateful we now have the support of the environmental law foundation and our solicitors, who have asked to take on our case for judicial review."
In a judicial review, High Court judges examine whether public authorities are acting within their legal powers.
They can order authorities to cease unlawful activities and can award damages.
The Marine Management Organisation, which regulates the marine industry, confirmed the campaigners have applied for a judicial review.
Campaigners fighting the dumping of dredged material from Devonport near a Marine Conservation Zone (MCZ) off Cornwall say their case is being taken to a judicial review.