The five-strong team of Fox-Pitt, King, Nicola Wilson, Zara Phillips and Tina Cook claimed silver after two clean jumps from Fox-Pitt and King.
Cook and King were unable to follow up with individual medals, however, each having a pair of rails down which dragged them outside the top three.
The medal was sealed by Cook’s round – although she picked up a time penalty which dropped her down one place in the individual standings – and the 41-year-old was delighted with silver.
“To be honest I was trying to focus on a clear round,” said Cook, who paid tribute to the vets that treated her horse Miners Frolic, who nearly died 12 months ago.
“The team, have done so well and it was so close – we could have got silver or nothing, and that would have been awful. Gold would have been brilliant, but silver is fantastic.
“It’s almost a fairytale. I can only say thanks to the vets that kept him alive and to the team at home that got him here – it’s been very stressful and a lot of grey hairs and wrinkles.
“It’s brilliant for equestrianism and for our sport. It’s great to see so many people here watching. I’ve got to get back in there and win an individual medal – that’s what I really want.”
Six-time Olympian King believes this ride was one of the most important she’s ever ridden as she all but confirmed silver for Great Britain.
The 51-year-old, winning her second silver medal, had a clear ride on Imperial Cavalier, but the experienced rider admitted it did all get a bit too tense.
She said: “That was probably the most important round I’ve ever done.
“You do what you have to do on the day I’ve been fortunate enough to do few championships, but this in front of our home crowd, who have been so support supportive, has been awesome.
“He did seem tense – he usually jumps high but he was jumping a little flatter. But he was a good boy and he jumped high enough, thankfully.
“We were hoping there was a chance of us overtaking the Germans, but they had put in a great performance and they deserved it and have done better than we have."
Phillips recovered well after she knocked fence number two, jumping a clear round from then on in, but the 31-year-old was still disappointed with her seven faults.
However, she paid tribute to her horse High Kingdom, who was in fine form, despite feeling under the weather when two shoes fell off after the cross-country.
“The whole week has been an amazing experience. He’s inexperienced horse and he’s coped with it really well – with the crowd, who have been unreal,” said Phillips, who is sixteenth in line to the throne.
Fox-Pitt, looking for a third team Olympic medal after silver in Athens and bronze last time out in Beijing, played a strong role as he had a clear round with no penalties, and he paid tribute to his own horse Lionheart, who struggled the day before.
“He’s come out bouncing today,” said Fox-Pitt.
“Something might have been amiss with him, but it was out of character for him, so I don’t know what was wrong with him yesterday and it was really disappointing.
“But he was fantastic today and we finished on a good note.”
Wilson had one penalty in her round after she also knocked fence number two over on Opposition Buzz, but still came in under the time allowed as she left the arena to rapturous applause.
Michael Jung then rode a controlled and flawless final round of jumping to take individual eventing gold while team-mate Sandra Auffarth nabbed the bronze.
Sara Algotsson Ostholt took the silver after an outstanding Olympic showing. The Swede lay in gold medal position entering the close contest but a knock-down on the last fence dropped her behind reigning world and European champion Jung.
Britain's King and Cook were third and fourth respectively going into the individual, but each had a pair of rails down, knocking them out of contention. King finished in fifth place, Cook in sixth.
Their royal team-mate Phillips, who drew a packed crowd and a huge number of journalists to Greenwich Park on Tuesday, fared better. A confident clear round vaulted her into eighth place from 14th going in.
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