A B767 CREW; DEPARTING LONDON (EGLL); FLEW THE SID THEY ANSWERED FOR IN THEIR READ BACK; ATC STATED THE SID FLOWN WAS NOT THE ONE THEY WERE CLRED FOR.

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I WAS THE CAPT ON DAY TWO OF A SIX DAY INTL TRIP WITH A PLANNED DEP FROM LHR TO ORD. FLT PLANNING AND ALL PREFLT CHECKS WERE COMPLETED. THE FPF WAS UPLOADED THROUGH ACARS BY THE FO AND VERIFIED BY ME. THE SOP FOR LHR IS TO CALL FOR YOUR ATC CLRNC (WHICH INCLUDES A SID ASSIGNMENT) WHEN THE FLT IS READY FOR PUSHBACK. AT PUSH TIME; THE FO REQUESTED ATC CLRNC. IT WAS RECEIVED; COPIED ON A NOTEPAD AND READ BACK AS FOLLOWS 'CLRED TO ORD FPR; COMPTON 5J DEPART; CODE XXX.' BOTH THE RELIEF FO AND I LISTENED TO THE CLRNC AND THE READ BACK. THERE WAS NO AMBIGUITY OR QUESTIONS AS TO THE CLRNC FROM ANY OF THE CREW. THE COMPTON 5J WAS LOADED IN THE FMC AND BRIEFED BY THE FO (PF). I ENTERED THE RAW DATA IN THE L VOR FOR BACKUP. AFTER WE WERE CLRED FOR TKOF; WE BEGAN EXECUTION FOR THE COMPTON SID. LHR TOWER DID NOT HAND US OFF TO DEPART CTL IN A TIMELY MANNER; SO I ASKED TWR IF WE SHOULD CONTACT DEP CTL. TWR STATED 'NEGATIVE; YOU ARE FLYING THE WRONG SID; YOU WERE ASSIGNED THE BUZARD 3J SID. FLY HEADING 275 DEGS; MAINTAIN 6000 FT. WE WERE HANDED OFF TO DEP CTL AND THE DEP WAS WITHOUT FURTHER INCIDENT. WX WAS VMC DURING DEP; NO OTHER TFC WAS OBSERVED; AND NO TCAS FA'S OR TA'S WERE RECEIVED. OTHER FACTORS: ALL CREWMEMBERS WERE EXPERIENCED IN LHR OPS. THE CREW WAS WELL RESTED AND ALL SOP'S WERE COMPLIED WITH. BOTH FO'S WERE PROFICIENT AND PROFESSIONAL. ACR FOM PAGE REQUIRES THAT THE DEPT SID NAME BE STATED ON INITIAL CONTACT WITH DEP CTL. THE LATE HANDOFF BY TWR PRECLUDED THIS SAFETY BACKUP FOR PROPER SID COMPLIANCE. THE LHR PROC OF ONLY KNOWING YOUR SID ASSIGNMENT AT THE LAST MOMENT BEFORE PUSHBACK COMPROMISES INSTALLATION; BRIEFING AND COMPLIANCE. IT WAS POSSIBLE THAT ALL THREE CREWMEMBERS MISHEARD THE SID ASSIGNMENT. HOWEVER; ALL CREWMEMBERS LISTENED TO THE CLRNC; AND HEARD THE FO READ BACK THE COMPTON 5J. CLR DELIVERY DID NOT CORRECT THE READ BACK IF IN FACT IT WAS DIFFERENT THAN THE ONE ISSUED. THE SID SHOULD BE PART OF THE UPLINK PROCESS. RECOMMEND LHR TWR ISSUE TKOF CLRNC AS 'CLR TKOF FLY XXX SID.'