Any idea what this is?

[deltarider]

Thanks, no alas I don't have the owners manual.

Have you tried to get one?

[beardylondon]

There’s a cb550 manual dated 1973 on this forum, which I downloaded. I haven’t really looked yet, only had the bike a month.

[deltarider]

Can you give us the internal diameter of that bracket, please?

[beardylondon]

internal diameter is 9mm

[deltarider]

Thanks, that's an indication it is not meant for the crankcase breather hose.

[deltarider]

I hereby pass on what Rainer informed me in the German forum. It explains a lot.
In Germany, there were two versions of the thick engine breather hose:

1st version: The hose is routed slightly to the left of the frame, above the carburetors, down between the engine and the swingarm, and then in front of the rear wheel. This worked until about the 1976 K2 models.

2nd version: After a veto by the German TÜV, the hose had to be routed away from the rear wheel and to the left into a bracket between the exhaust pipes. The bracket was attached to the left footrest, and there is no Honda part number for it. This applies to the late K2 models (1977) in Germany. It was probably another special German TÜV requirement.
So, it seems that p.170 in the Shop Manual CB500-550, which "says" to be about the CB550K2 is in fact (also) about the CB500K2 '76 as all the modifications presented there, are also on my CB500K2-ED. The following pages listing the specifications is about the CB550K2 only however.
So the modification of that particular bracket came on the very last CB500K2 [-ED, -F, -G]. Rainer states that particular bracket had no partnumber. I think it may have been: 90514-323-610 as far as the CB500K2.

 (picture courtesy: Rainer K)

[deltarider]

To conclude: both the CB500K2 (76-77) and the CB550K2 (76) had a guide bracket there. The one on the first model was to guide the big crankcase breather tube, the one on the 550 was to guide another smaller tube and had PN: 90514-374-700. I think we've finally got it solved. (Phew!)