The Royal Navy has insisted HMS Turbulent was in Devonport Naval Base throughout the day.
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Permission for the incinerator in Devonport was granted last year by the previous Conservative administration.
Bidders had until 23 January to register an interest in the former Devonport-based ships.
The Royal Navy insisted HMS Turbulent was in Devonport Naval Base throughout the day.
Tritium is a radioactive substance produced by the reactors from nuclear-powered submarines based at the Devonport yard.
Depending on the outcome of the review, it could mean changes to the tritium discharges at Devonport.
Their aim is to complete the 800-mile (1, 287km) trip before the ship returns to Devonport on Friday morning.
Devonport is home to the Royal Navy's seven Trafalgar-class nuclear-powered submarines and has four decommissioned nuclear submarines awaiting dismantling.
The ship will undergo a short maintenance period at Devonport before returning to her ocean deep survey hydrographic duties.
Five sailors from Devonport-based HMS Sutherland have set off on foot from Scotland to race their ship back to Plymouth.
The MoD wanted the listing to be postponed, fearing that it could threaten Devonport dockyard which is operated by KBR.
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The yard has struggled to find new work since it was taken over by Devonport dockyard owner DML in 2004.
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German company MVV Devonport Ltd was awarded the contract to build the plant at the Devonport North Yard last year.
Plymouth is headquarters of 3 Commando Brigade and Devonport in Plymouth is home to the largest naval base in western Europe.
It is one of a number of historic features, like Drake's Leat and Devonport Leat, which took advantage of Dartmoor's gradient.
Across the South West, the biggest margin on a project is new accommodation for services' personnel at Devonport Naval Base in Plymouth.
Deployment began on 30 September, 2010 when HMS Cumberland left the Royal Navy base at Devonport and headed towards the Arabian Gulf.
It is the last of the four Devonport warships being scrapped - with HMS Cumberland, HMS Chatham and HMS Campbeltown already gone.
It owns and runs some British defence facilities, including the Devonport naval shipyard, provides logistical support and maintains submarines for the Royal Navy.
The navy is open to offers for the former Devonport-based ships, including being scrapped and recycled, reused or sunk to become artificial reefs.
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Planning permission for the waste-to-energy plant at Devonport North Yard in Plymouth was granted last year and building work is due to start soon.
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Walking around Devonport, most of the public did support the navy's continued role, though they were aware of a subtle PR exercise going on around them.
The navy said the equipment, built by BAE Systems at Devonport and at HMS Collingwood in Fareham, Hampshire, would be used by about 1, 000 new trainees a year.
People attending the meeting heard calls for reductions in the amount of radioactive chemicals released from Devonport Dockyard and concerns about what might happen if there was an accident.
Staff at Mayflower Marina in Devonport battled for a number of hours to upturn part of a wooden pontoon which had become trapped on sunken columns that anchor it after having been twisted by the wind and waves.
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