1. That's not a MUST.
2. Some puffins (crossings with near-side panels) here have green bike symbols on their panels.
3. It's blooming stupid to dismount and wheel where a pelican, puffin or zebra connects two cycleways (as they often do, at least around here, because some highways officers are a bit careless about cycling) because we are normally allowed to cycle on the carriageway there anyway as long as we give way to walkers. Dismounting just makes cyclists a wider, slower, less-controlled annoyance for all other road users.
3. Dismounting and wheeling would be even more stupid if you are going along the carriageway, crossing the other road (the cycleway or bridleway, which is also a road in law).
That's one rule I suggested correcting during the consultation period, but they've kept the stupid version, probably because it's shorter and only advice anyway... but it's still the Highway Code equivalent of a "CYCLISTS DISMOUNT" at every puffin on a cycleway.