They travelled to the Kingdom by train where a crowd of several hundred had gathered around Aberdour Railway Station to greet them as they arrived in the Royal Train.
As the Royal couple descended to the red-carpeted platform, they were greeted by Sir John Gilmour, Lord Lieutenant of Fife, who presented to them the official party of dignitaries.
After the brief round of introductions the Queen and Duke emerged from the station to be met with loud cheers from the crowds.
She was presented with a posy of flowers from four-year-old Sarah Taddie, of Aberdour Playgroup.
Sarah was accompanied by Katherine Cochrane (12) and Peter Coach (5), of Aberdour Primary School, Janet Jenkins (11), of Starley Hall School, near Aberdour, and Jacqueline Aird (1 1), daughter of British Rail area traffic manager Andrew Aird of Thornton.
Then, after thanking the children, and a wave to the cheering onlookers, it was off to Braefoot Bay where it was a right Royal day for many employees – and for their families – who turned out in force for the official inauguration, the Queen and Prince Philip stopping to chat to many of them as they toured the site.
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Tight security greeted the arrival of the Royal guests for the ceremony, where they were welcomed by the Dysart and Dundonald Pipe Band and the 300-strong flag-waving crowd on the roof of the blast-proof , building.
In attendance was Secretary of State for Scotland Malcolm Rifkind and top executives of Esso and Shell worldwide.
After the presentation of a line-up of VIPs, the Queen and Duke of Edinburgh –with Sir John and Chief Constable William Moodie, following on – viewed the site
Then the big moment came for eight-year-old Dalgety Bay schoolgirl Claire Paton who had the honour of presenting a bouquet to the Queen after winning a safety poster competition.
They Royal party then moved on to spend half and hour touring the nerve centre of the complex, before setting off by Range Rover for a tour of the vast complex, donning safety glasses as they stepped to look inside one of the six huge furnaces.
All the way, their progress was shown via closed-circuit television on a giant screen with TV presenter and Mastermind host Magnus Magnusson providing a running commentary.
The final destination was the official inauguration ceremony where they received a trumpet fanfare from John Wallace from Glenrothes, principal trumpeter with the London Philharmonic Orchestra, and colleagues John Miller, from Markinch, Nigel Boddice and Eric Dunlea.
The Queen was invited to accept a copy of a specially commissioned film, describing the development of the plant.
After the formal speeches, and amidst all the complex technology, the Queen pulled a simple cord to unveil the plaque which commemorated the event.
The Royal couple, accompanied by Lady in Waiting the Duchess of Grafton, Equerry Major Hugh Lindsay, and the Queen’s Private Secretary, Sir William Heseltine, were more than half an hour behind schedule when they left Mossmorran after lunch.
As the visit came to a close, Prince Philip took the wheel of their private Range Rover, with the Queen in the front seat and their chauffeur in the back, as they drove out of Fife and headed north for Balmoral.