When she finally arrived home, thousands of people lined the banks of the River Avon to see her towed back under Brunel's famous Clifton Suspension Bridge.
Using archive footage and the personal memories of the people who were involved in the salvage effort, the programme pieces together the dramatic story of how the ship was brought home.
At first it seemed an impossible task - the rusting iron hulk of the Great Britain was lying abandoned in Sparrow Cove, a desolate corner of the Falkland Islands.
But with financial support from millionaire philanthropist Sir Jack Hayward a team of salvage experts from the United Kingdom and Germany was assembled.
Their first challenge was to remove the ship's giant masts - a task that nearly ended in tragedy when the mizzen mast crashed down unexpectedly onto the deck, destroying a cook house.
Horst Kaulen, who was leading the German half of the salvage team, recalls: "It was important to take the masts down for transportation because the centre of gravity was too high. So we tried to pull the masts out of their sockets.
"When it didn't go as planned the emotion came up, then I threw my hat on the floor and swore".
The bow of the Great Britain is like a clipper ship. It's a really beautiful piece of naval architecture covered in barnacles
Even once the masts had been removed, Brunel's ship was in no fit shape to be refloated - there was a gaping crack in the side of her hull.
The salvage team hit on the idea of asking the Falkland Islanders to donate used mattresses to help to plug the hole.
It was an unconventional approach, but eventually it worked and the ship broke free of the seabed for the first time in nearly 40 years.
Malcolm Macleod was leading a detachment of the Royal Marines in the Falkland Islands and helped out with the operation.
He remembers the emotion of seeing the ship rise up onto the pontoon to begin the journey back to Great Britain.
"There was a moment when the bow of the ship broke surface and the sun was shining on the bow.
"The bow of the Great Britain is like a clipper ship. It's a really beautiful piece of naval architecture covered in barnacles. I was just completely spellbound by that sight".
After 8,000 miles at sea, ss Great Britain finally made it back to Bristol in July 1970.
A huge crowd welcomed her home as she was towed under the Clifton Suspension Bridge and back into the dock.
Thousands of people lined the banks of the Avon to welcome the ship home
Horst Kaulen said: "The bridge was full of people, bells were rung, there was applause, people threw confetti in paper strips in celebration which floated down onto the Great Britain.
"I've never seen anything like that again. It was simply gripping."
Forty years later, the ship has been transformed into an award-winning tourist attraction, bringing thousands of visitors to Bristol every year.
The ss Great Britain Trust has created a new exhibition to celebrate the 40th anniversary of the ship's homecoming.
Using a grant from the Heritage Lottery Fund the team has been working on an ambitious oral history project, collecting memories of the homecoming.
• When Brunel's Ship Came Home can be seen on BBC One in the West of England at 7.30pm on Monday, 12 July. The programme will also be available on the BBC's iPlayer service for seven days after the original transmission.
• On Sunday, 4 July at 9am, BBC Radio 4's
includes an interview with the Duke of Edinburgh about his memories of standing on the deck as the ship was edged into the docks.
• On Monday, 19 July, BBC Radio Bristol will be marking the anniversary by going back to the 1970s - flares are optional.
The station will be throwing out its normal playlist to deliver a day of music from the seventies. There will be guests and features related to the ss Great Britain throughout the day.
Steve Yabsley will investigate the gadgets, fashions and fads of the 1970s while Peter Rowell will be joined by some of the leading actors, performers and personalities of the time.
Ben Prater's drivetime programme will come live from on board Brunel's ship as the anniversary celebrations get under way.
• The July issue of
BBC History Magazine
includes a profile of the celebrated engineer Isambard Kingdom Brunel and a look at one of his other ships, the ss Great Eastern.
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