The government confirmed it no longer required that particular model, known as BlueSky.
"We are no longer supporting the production of the BlueSky device following a reassessment of the product's viability in light of the ever developing picture around what is needed to most effectively treat COVID-19," said a spokesman for the Cabinet Office, which is coordinating ventilator orders.
"We are continuing to work at unprecedented speed with a number of other manufacturers to scale up UK production of ventilators," the spokesman said.
The government has appealed to industry to come forward with new models of ventilator that could be produced on a large scale at short notice to help the National Health Service deal with a surge in patients infected with the new coronavirus.
More than 30,000 ventilators in total have been ordered from various consortia of firms from sectors including aerospace, engineering and Formula One.
The source, who did not wish to be named because they were not authorised to disclose sensitive details to the media, said the group involved in the BlueSky project had been preparing to deliver thousands of units.
The source said the reason given by the government to the BlueSky team for cancelling the order was that while the overall number of new UK coronavirus infections was slowing, cases seen in hospitals were more complex than expected.
With several projects competing for the same components, which are in limited supply, the government decided to prioritise more sophisticated devices and cancel the BlueSky order with immediate effect, the source said.
The government is going ahead with the production and delivery of other devices as part of its initiative with industry. The first paraPac devices from Smiths Group were delivered to hospitals on Sunday.
Other devices are currently going through testing, including newly designed products. The government has said it will confirm orders once the new devices pass approvals and have confirmed delivery schedules.