Would the Bristows guys already at the bases have a good chance of retaining their jobs?
Yes. EU law binds the new contractor to take on the employees of the old contractor whose jobs were dedicated to the said contract.
Sadly it doesn't work like that. The loss of a contract does not mean that the employees are covered by TUPE, TUPE is only relevant when the company itself is taken over, then the terms and conditions of the employees are protected.