I know these are not RAF, but…

In January 1929, the US Army Fokker C-2 ‘Question Mark’ remained continuously airborne for 150 hours and 40 minutes, corresponding to nearly a week aloft. During this time the engines consumed 5,812 U.S gallons of fuel.

The tanks on the aircaft were of course insufficient for such an amount, so the Question Mark was refuelled in the air at intervals. In total, more than 20 tons of goods were transferred to the Fokker in the air by other aircraft. On 7 January, an engine failure forced the record flight to be terminated. By then the aircraft had been refuelled 37 times.

The crew consisted of Chief Pilot Major Carl Spaatz, First Pilot Ira C. Eaker, Pilot Lieutenant Harry A. Halverson, Pilot Lieutenant Elwood R. Quesada, and Flight Engineer Sergeant Roy W. Hooe.

On Feb. 26, 1949, Capt. James G. Gallagher and a 13-man crew took off from Carswell AFB, Texas, in a B-50 bomber named Lucky Lady II. 94 hours, one minute later, they landed back at Carswell, having completed the first non-stop “around-the-world” flight. They refuelled 4 times from KB-29s.

On 24–25 November 1956, four B-52Bs of the 93rd BW and four B-52Cs of the 42nd BW flew nonstop around the perimeter of North America in Operation Quick Kick, covering 15,530 statute miles (13,500 nm, 25,000 km) in 31 hours 30 minutes (493.0 smph). SAC noted that the flight time could have been reduced by 5-6 hours if the four inflight refuellings were done by fast jet-powered tanker aircraft rather than propeller-driven KC-97 Stratotankers.

On Jan. 18, 1957, three B-52 Stratofortresses completed a 24,325-mile around-the-world nonstop flight, nicknamed Operation Power Flite, in 45 hours and 19 minutes, with several in-flight refuelings by KC-97s, at an average speed of 534 mph.