Incorrect, The first successful jet aircraft, the Heinkel He 178, flew only five days before the start of the war, on 1 September 1939. The first German Jet fighter was the ME 262
The first jet fighter to be developed in the United States was the Bell P-59 Airacomet; its maiden flight took place on October 1, 1942, about 5 months earlier than the date on which the British Gloster Meteor first flew.
In Great Britain, a Royal Air Force officer, Frank Whittle, invented the gas-turbine engine that would power the first British jet, the Gloster E. 28/39, which made its first flight on May 15, 1941.
The Gloster Meteor went into full production 12 January 1944, the first Meteor F.1, serial EE210/G, took to the air from Moreton Valence.
The de Havilland Vampire is a British jet fighter which was developed and manufactured by the de Havilland Aircraft Company. It was the second jet fighter to be operated by the RAF, after the Gloster Meteor, and the first to be powered by a single jet engine.On 20 September 1943, the first DH.100 prototype, serial number LZ548/G, conducted its maiden flight from Hatfield Aerodrome; it was piloted by Geoffrey de Havilland Jr., the company's chief test pilot and son of the company's founder. This flight took place only six months after the Meteor had performed its own maiden flight; the first flight had been delayed due to the need to dispatch the only available engine suitable for flight to America to replace one destroyed in ground engine runs in Lockheed's prototype XP-80 jet fighter.
If the Air Ministry had listened to Frank Whittle the Battle of Britain could have been fought with RAF jet aircraft instead of piston powered.