The thicker rings are leaking. That sweeps the top of the pistons, removing the carbon. In time, this will also cause a burn to start down the side(s) of those pistons, which will ruin them.
The carbon is normal, especially if the engine has not seated the rings yet (1000 miles is barely enough for that process), and if is has not been revved enough to blow out the carbon. Excessive buildup, though, can come from a too-high carb float level (i.e., the fuel needles wore a little, need some adjustment), too rich idle mix (air screws should be at 7/8 to 1 turn out on K2), late spark timing or weak spark (burned points) or with Dyna 'S' ignitions on stock Honda coils and lots of slow riding (i.e., weaker than stock spark comes from using Dyna 'S' triggers: don't know if yours has these?).
I have seen carbon as thick as 1/8" (that's U.S. inches
) on top of 750 pistons, with no ill effects besides frequent plug fouling, though. And, a long hiway trip usually clears this up. If you have a paper air filter, beings as how you're in foggy Britain, the filter will not flow as well as the mainjet expects there: I often dropped the mainjets a full 10 size in humid climes to improve the carbon issues.
What mainjet size do you have? On a K2, I would expect either a 100, 105, or 110: the early K2 had 110, the "middle" of the production had 105, and just before the K3 appeared, they had 100, along with the short-production 7-chamber exhaust pipes. You can see how many chambers your mufflers have by counting the little spotweld dimples along their length: inside the pipe, there is a baffle at each dimple. The HM341 pipes came in 4, 5, and 7-baffle versions: the set I bought last year (new) has 5, for example. My original ones had 4 baffles, the carbs had 110 mainjets. When I replaced the pipes in late 1972 because of an accident I had, they were the 5-baffle types, and I had to go to a 105 mainjet: Honda had also done this in production about that same time. Today, at altitude, I run with 100 mainjets (6000 feet where I live), and I don't have the carbon issues.