The section of the rocket carrying its three altimeters was found just five kilometres (three miles) away and the rocket engine eight kilometres (five miles) away.
UK rocketeers have smashed the British and European amateur altitude records.
The Mars (Middlesex Advanced Rocketry Society) team sent their Phobos-EAV vehicle soaring to more than 10,668 metres (35,000 feet) over the Black Rock Desert, Nevada, US.
The rocket, which flew to the tune of Elgar's Land of Hope and Glory, more than doubled the previous UK mark held by a group of rocket enthusiasts from Sheffield.
And it comfortably bettered the previous, highest, verified altitude known to have been achieved by a European-built amateur rocket, which stood at about 6,100 metres (20,000 feet).
Mars Project Director Ben Jarvis, from Pinner, said: "There is such a history of the British coming here in record-breaking teams. We are proud to be part of that tradition."
Peak altitude
This was a reference to the world land speed records set at Black Rock by British drivers such as Richard Noble and Andy Green.
"But it was an absolute success and we are absolutely astounded by how well it went. We are ecstatic.
"We also found the rocket again very quickly after it landed - people can take days to find them out there and sometimes they never find them at all.
"But someone saw ours come down and it was only 10 minutes' drive away."
Celebration rocket
The section of the rocket carrying its three altimeters was found just five kilometres (three miles) away and the rocket engine eight kilometres (five miles) away.
The launch was witnessed by US rocketry groups and the data will now be sent to the UK Rocketry Association for official verification.
"We were a bit disappointed the rocket didn't go to 15,240 metres (50,000 feet), but the disappointment only lasted 10 or 15 seconds," Mr Jarvis said.
"We had a smaller rocket as a back up plan in case the big one failed but we flew it anyway and it went to 16,000ft."
Higher goal
The Phobos-EAV rocket stood at just over 3.6-m (12-ft) tall and was only 10 centimetres (4 inches) in diameter.
The booster motor in the rocket was custom built by an American company and was delivered to the team on their arrival at the launch site on 28 September. The motor was designed to deliver an average thrust of one metric tonne, sufficient to propel the 24-kg (50-lb) rocket to a speed in excess of 3,220 km/h (2,000 mph) - almost three times the speed of sound.
A slender 1.8-m (6-ft) long "dart" mounted at the front of the vehicle was released after the motor shut down and coasted, under its own momentum, to a peak altitude of well over 35,000 ft.
The Mars group now want to launch a rocket to over 30,400 metres (100,000 ft) next year.
"We want to add another digit to the altitude we have got so far and I think 30,400 metres is definitely on," said graphic designer Mr Jarvis.