From an article on FlightGlobal.com, we learn these particulars about the flight:
The flight, captained by Capt Rod Mitchell, took 18h 45min to reach Melbourne, during which three hot meals were served. It has not been released how many passengers were onboard the 305-seat aircraft, although the prime minister usually travels with around 40 members of entourage and is followed by a further 20 journalists. To comply with crew flight time limitations, 20 crew were onboard, of which two were captains, two were senior first officers and 12 were cabin crew. An engineer, a security manager and a catering manager were also part of the personnel.Mr. Blair and his party were flying to Melbourne to attend the Commonwealth Games.
In June last year Boeing flew the 777-200LR variant 21,601km in 22h 42mins without refuelling from Hong Kong to London, setting a new record for a commercial airliner. However the 24 March London to Melbourne flight is the longest flight with paying passengers under civil transport rules.