Is there a precedent in the UK for such a mass sacking, or at least a threat of it?
If the sacking threat is made, then surely the reality will be that those who fail to show up for their shift will claim they are sick
Yes and as recently as June this year. 900 got the boot at an oil company (all re-instated after negotiations though). I would rather suspect going sick on the day of the strike would lead to the same outcome - large companies can be pretty ruthless. Act now, clear up the mess later.