March organisers said 284,500 people took part in the day the countryside came to town. The Edinburgh team took video grab pictures of marchers at three-minute intervals throughout the five-hour event and found marchers were travelling at 1.07 metres a second and passing the monitoring point at the rate of eight marchers a second.
A 3.7m wide strip of the route contained a mean of 27.49 people in the 100 video grabs, with the flow of marchers altering only slightly during the event. The researchers, from the university's computer studies department, calculated the numbers on the march were between 133,118 and 151,400.
Yesterday the Countryside Alliance said the researchers needed to "check their methodology". Spokeswoman Janet George said eight monitors had counted each line of marchers as they left the start. "We have done our own very, very careful count," she said. "[The Edinburgh researchers] are wrong by a very long way."
Scotland Yard estimated the turn-out at 250,000. A spokesman said it was the guesswork of experienced officers. "It's very difficult and is always an approximation," he added. The technique was inspired by methods used by marine scientists to count seals on beaches.
Mathematician Russell Leaper said the team hoped to use their methods to measure other demonstrations. "People have been assessing the level of support for these events using very, very poor evidence. Every time there is a major demonstration there is a big argument about the numbers."
The researchers said their work had been helped by the fact that the crowd was carefully controlled and that the "flow rate and march speed were much more consistent than might have been anticipated".
It was admitted that some of the walkers may have dropped out of the march soon after the start, before reaching the monitoring point - 2km down the route - and thus not been counted.
The Edinburgh study was commissioned by the Campaign for the Protection of Hunted Animals, which was opposed to the march.