I had something a little similar once when my road home was closed because of a gas leak. A polite enquiry to the police officer on duty elicited the response that I could go through as long as I didn't smoke, which seemed fair enough. Residents were bringing out cups of tea to the gas workers and emergency services, so it can't have been massively dangerous.
Isn't there a factor here about obeying the reasonable instructions of a police officer? If there's a bad accident, instructions to go around are likely to be "reasonable". It's a decent argument that, if pedestrians are allowed through, so should cyclists be on foot. However, the judgment of the police officer about whether the necessary detour was more "reasonable" for a cyclist than for a pedestrian would also come into play.
I don't think you could cite Crank v Brooks in this situation as conclusive that a cyclist on foot is a pedestrian; it considered a very particular context in which a motorist tried to escape blame for hitting someone pushing a bike across a crossing, on the basis that the victim was a cyclist and should not have been there. That said, there is now general acceptance that someone pushing a bike should do so (carefully) on the pavement, whereas, when I was growing up, there was still a certain expectation that you would walk on the pavement and push the bike in the gutter. But these are all assumptions untested in court. I don't think the law actually gives any fixed answer, and I'm not about to be the one in court extending case law.
In summary, if you disobey or challenge a police officer's instructions, it may go badly with you, and you don't really want to end up in court arguing the toss. Trying to stand on your rights, and deploy dubious legal cases to force your point, is likely to be a less-successful tactic than a plea that it's cold, it's wet, it's a long way round, and you promise not to be any more trouble than those pedestrians walking through.