It wouldn't need the numbers to be all that serious. It would need Spokes, PoP, CTC, Sustrans and similar organisations to publicly state that they were no longer going to be a party to cyclists' deaths by condemning the reasonable use of pavements as an alternative to the roads.
They could say that since Government had systematically failed, refused, to make adequate provision for cyclists' safety on roads, and had systematically failed to enforce the law even in situations where the death of cyclists was plainly the fault of motorists, that they were no longer going to condemn people who chose to cycle on pavements provided they did so with consideration for pedestrians.
They could say that they were going to recommend to cyclists that in circumstances where they felt that the road was too dangerous they should mount the pavement to get past potentially dangerous situations. But that they should do so carefully, cycling at walking pace and giving way to pedestrians.
They could do this while still recognising that the pavement was designed for pedestrians and that cyclists using the pavement creates the potential for conflict but that cyclist / pedestrian conflict was much less likely to be deadly than the current situation of conflict between vehicles and bicycles.
They could say that they recognise that pavement cycling is illegal and that cyclists might be fined. They could advise cyclists receiving fixed penalty notices to refuse to pay them and take the cases to court. I suspect they'll never get there (because they won't get past the public interest test in taking them to court) but if they do, the cyclists would be supported financially and defended, provided their actions were reasonable (see above).
They could tell people who wanted to cycle but who were afraid of the road to cycle on the pavement.
That would certainly make the point publicly and be noticed by the press and politicians. It would be both civil and disobedient and to the extent that reasonable cyclists did it - cycled on the pavements in situations that would be dangerous - it would be effective at least in keeping some cyclists safer than they would be on the roads. It would need one case - just one where a jury refused to convict a cyclist for riding on the pavement as an act of self-defence.