Captain exercises his emergency authority to deviate around a thunderstorm on the North Atlantic Tracks; after a request to Shanwick Oceanic via CPDLC is denied. Shanwick indicated that a loss of standard separation occurred during this incident.

Narrative

Shortly after returning from my rest period (2nd break); we were at FL350; SLOP [strategic lateral offset program] R1 off Track W. We saw green and yellow radar returns indicating thunderstorms (TRW) building ahead; with tops at/near our altitude on our route of flight. After evaluation we determined that we needed to deviate altitude or course to avoid possible turbulence and adverse weather. [We] requested CPDLC altitude change to climb above radar returns (yellow/green) ahead. Shortly after requesting; Shanwick's CPDLC response was 'Unable due to traffic'. [We] continued on SLOP R1 analyzing weather and options. Determined I needed to utilize emergency authority to deviate. Eight minutes later began deviation from R1 SLOP to R12 to remain clear of buildups/cloud ceiling/yellow radar returns directly ahead. Focus was outside looking for possible aircraft and monitoring track/course deviation. Five minutes later sent CPDLC free text message; 'DV8ing 12 south for TRW.' [We] remained at FL350. Transmitted on 123.45 our position; altitude and deviation distance off Track W. Received two SelCal's from Shanwick; but upon attempting to communicate; Shanwick was unreadable. (Solar storm was impacting HF.) Several minutes later; answered another SelCal and was advised that Shanwick 'was filing' on the incident because our deviation had violated standard separation with two other aircraft. I asked for the flight numbers of the other flights; which was provided. Requested separation distances and after several minutes; was told 'Shanwick is too busy. It will be in the report.' Contacted these flights and plotted their positions at the time in question. (Note: All aircraft 'involved' were at FL350; Mach .83.) [There appeared to be no loss of separation.] We were in day VMC at all times; just above a cloud deck and deviating to the right of the TRW; lights on; at FL350. 'Aviate; navigate; communicate' priorities dictated that we avoid the cells as our first priority; and maintain traffic watch as a second priority. Contacted Dispatch on Satellite Phone and informed them of situation. They indicated that they had received some message traffic on the incident.