B777-200 pilot flying reported maneuvering one mile left of course after encountering wake turbulence from a preceding aircraft in cruise flight.

Narrative

As we were approaching GOMUP at FL330 there was an aircraft 2000 feet higher converging. I thought they would be passing but they turned on to the same course as us. We were faster - as the gap closed we started to encounter ripples of the aircraft's wake. The prevailing winds were left to right and as we gained on the traffic it seemed that the wake ripples increased. I felt we did not have enough time to request a clearance and in the interest of safety I decided to maneuver our aircraft left 1 mile to avoid the wake. I felt going right would increase the risk of flying directly into the preceding aircraft's wake and possibly putting us into an upset situation. We were one mile left of course for approximately 20 miles and returned to course. I did send a CPDLC message to Shanwick Oceanic to advise we were back on centerline of route. I do believe when we were maneuvering the route confirmation was sent and mistakenly accepted.Shanwick Oceanic should give aircraft some lateral distance crossing oceanic fixes.