Let them strike
Fujitsu (for example) run some Government IT.
Fujitsu staffers go on strike.
That does not mean that Government IT goes on strike - even those bits provided by Fujitsu.
I would expect all Government outsourcing contracts to specify the required service levels and also to specify a regime of service credits to be paid in the event of the contractual service levels not being met.
Fujitsu surely have an obligation to ensure that all required systems are up and running, even if their staff on strike.
Could work out expensive if a strike day were to coincide with a high volume workload day.
(AC because I don't want anyone coming after me if by some chance all the IT falls over on the first strike day. Nothing to do with me, guv.)