Meggitt, which employs 12,000 people and builds components including oxygen systems for civil aerospace and military fighter programs, is leading one consortium alongside engineers GKN, Thales and Renishaw.
The other two teams are being led by carmakers McLaren, which is looking at how to design a simple version of a ventilator, and Nissan, which is working with others to support existing ventilator producers.
European aerospace group Airbus is working across the process to see if its 3D printing or production facilities can be of use.
"The aim is for there to be a prototype in two weeks and for manufacturing to start in four weeks," one person familiar with the situation said.
With the coronavirus outbreak taking hold in Britain, Prime Minister Boris Johnson turned to industry earlier this week, asking major companies such as Rolls Royce and Ford to build ventilators that are critical for helping those who are struggling to breathe.
The head of the National Health Service said on Tuesday that Britain had 8,175 ventilators in the country.
Two groups are acting to coordinate the program - PA Consulting and High Value Manufacturing Catapult which was set up by the government to bridge the gap between British business and its powerful academic sector to turn ideas into income.
Airbus said these were unprecedented times and it would help where it could. "Our engineers and technology teams are investigating the practicalities of how we might best support the design, manufacturing and assembly of critical medical equipment," a spokesman said.
The car companies are looking at how they could help with production of a simplified design of a ventilator, analyzing existing models and looking at ways to develop a prototype quickly.
The government has approached carmakers including Jaguar Land Rover, Ford, Honda, Peugeot-owned Vauxhall, Bentley, Aston Martin and Nissan in the last few days.
McLaren has offered its design and engineering expertise. Others are on standby and waiting for more specific demands from the government.
(Writing by Kate Holton; editing by Michael Holden and William Schomberg)
By Sarah Young and Costas Pitas