A factory shipyard increases annual output without building ships in days

Would that factory-style infrastructure let the Royal Navy replace a carrier during the Falklands War in three days?

No. The useful gain would be a steady flow of completed ships: the cruiser example envisages twelve ships in production and roughly six commissions a year.

A factory-style yard would still need years to finish each warship. Its advantage would come from keeping many ships moving through the same production process at once. The hypothetical cruiser yard has twelve ships in production, a launch-to-commissioning interval of roughly two years, and an eventual output of about six ships a year. Common hulls, machinery, bridge structures, and funnel arrangements would leave the weapons fit as the principal difference between variants. One ship in every three could receive anti-aircraft armament as requirements changed. Sustained output from that yard would let other yards concentrate on other construction.