To be legally enforceable, I understand a zebra crossing must have Belisha beacons but does not need the zebra stripes. That said, the white stripes are not actually illegal without a Belisha, and they make the crossing more visible to all but the most "head-down" cyclist (who would be on the main carriageeway anyway), warning users of a possible conflict with pedestrians. And, after all, even the most "furious" cyclist would realise that a collision with a pedestrian is something to be avoided - it is likely to cause delay: and the cyclist often comes off worse anyway.