Davey, 23, has made 23 first-team appearances in the last four years, while academy graduate London, 24, has played 12 first-class matches.
Angus Fraser, Middlesex managing director of cricket, said: "Releasing Adam and Josh was a tough decision.
"However, young cricketers do get to an age when they need to be playing regular cricket."
He continued: "Adam and Josh are at this stage of their careers and are yet to claim regular first-team places.
"At Middlesex, we have several talented younger cricketers coming through and they now deserve the chance to push their credentials forward.
"Middlesex thanks Adam and Josh for all their effort and time and wishes them well in the future. They will always be welcome at Lord's."