The video, issued by the military wing of the 1920 Revolution Brigades, also showed an explosion at a distance and what appeared to be the debris of a plane on the ground.
Aljazeera said on Monday it had received a copy of the tape from the group.
The Royal Air Force C-130 Hercules went down at 4.40pm (1340 GMT) on Sunday, according to the military press office in Baghdad.
Military sources told Britain's domestic Press Association news agency the number killed in the crash was 10. The British government later said nine Royal Air Force personnel and one soldier were missing and believed dead.
The crash is Britain's biggest single military loss since the invasion of Iraq in March 2003.
Earlier, al-Qaida-linked group Ansar al-Islam posted a statement on a website claiming it downed the aircraft.
The video alleges the missiles
are being fired at the plane
The authenticity of the website could not be verified.
British Defence Secretary Geoff Hoon said in a statement: "We are aware of reports that the aircraft may have been shot down, but we are not in a position to come to any conclusions until the investigation is complete."
The defence ministry said earlier a thorough investigation into the cause of the crash had begun and that experts were due to examine the site again on Monday.
Report of bomb
A report in a British newspaper late on Monday said that the plane was downed not by missiles but by a bomb planted on board.
The Sun newspaper said it had been told the plane exploded at an altitude of 4500m, too high for such a missile to strike.
Citing what it called a "senior Ministry of Defence insider", the paper said military investigators were instead looking into whether a bomb had been placed inside the plane.
"It is clear the C-130 exploded in mid-air and shattered into
thousands of pieces," the source told the paper's Tuesday edition.
"A bomb could have been planted on the plane when it refuelled in Baghdad and stopped to collect passengers and cargo."
SAS on board?
An officer with the US-led military in Baghdad said the plane had been flying to Balad, which lies 70km north of Baghdad.
The wreckage covered a wide
area, suggesting impact in the air
Balad houses one of the largest US air bases in Iraq and has two runways, according to Britain's Press Association.
The ministry also declined to comment on reports in The Daily Telegraph and Daily Mirror newspapers that members of Britain's elite Special Air Service (SAS) were aboard the flight.
Air Vice-Marshall Tony Mason, a military expert, said the crash, which occurred during a spate of attacks aimed at sabotaging the first democratic elections in Iraq for 50 years, could have been caused by hostile action.
"On the face of it we have a fully serviceable aircraft, we have an extremely competent crew, we have the potential indicator that the first statement said the crash site covered a wide area, which suggests impact in the air rather than the ground," Mason said.
On Monday, The Daily Telegraph said: "It was not immediately clear what caused the crash but the most likely explanation seemed to be that it had been shot down by insurgents."