ACR ON VECTOR ENTERS MIL AIRSPACE RESULTING IN INTERCEPT AND TCASII RA. ARTCC LOST TRACK OF ACR ON HDOF BTWN CTLRS.

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LONDON CTL WAS VERY BUSY AT THE TIME OF CONTACT; GAVE US A HDG OFF AIRWAYS FOR TFC. AFTER APPROX 15 MINS; BOTH PLTS NOTICED WE WERE SIGNIFICANTLY S OF COURSE -- NECESSARY TO MAKE OUR ATLANTIC XING ENTRY POINT. CAPT (PNF) QUERIED CTR ABOUT HDG. TOLD TO REMAIN ON HDG BY CTR. MOMENTS LATER; RECEIVED TCASII RA AND RESPONDED TO CLB. TFC BEHIND AND UNDER US CLBING TOWARD US. PNF DECLARED TO CTR THAT WE WERE RESPONDING TO TCASII. THIS WAS NEW CTLR WHO SEEMED CONFUSED AS TO WHO WE WERE; THEN GAVE US TURN TO OUR ATLANTIC ENTRY POINT; TOLD US TFC WAS MIL FIGHTER COMING TO INTERCEPT AND CHK US OUT AND GAVE US FREQ THAT WE SHOULD BE ON. WE HAD CLBED TO FL320 DURING OUR RA; TRYING TO AVOID THE TFC WARNING. IT SEEMS THAT THE FIRST LONDON CTLR EITHER MISSED HANDING US OFF; OR GOT OUR FLT NUMBER CONFUSED WITH SIMILAR ONE OF SAME CARRIER AND WE WANDERED INTO MIL AIRSPACE. WHEN CTLRS CHANGED; NEW ONE HADN'T ANY IDEA WHERE WE WERE; THOUGHT WE'D BEEN SWITCHED. POSSIBLE FACTORS: VERY BUSY FIRST CTLR. SIMILAR CALL SIGNS. CTLR CHANGE WITH POSSIBLE INFO (ABOUT US) MISSING DURING THE XFER. AGGRESSIVE FIGHTER INTERCEPT CAUSING RA AND RESPONSE. I'M CERTAIN THAT WE DIDN'T MISS THE FREQ XFER IF THERE WAS ONE SINCE WE WERE BOTH VERY AWARE OF BEING SO FAR S OF INTENDED TRACK AND PNF QUERIED 2 TIMES ABOUT REMAINING ON THAT ASSIGNED HDG.