What Royal Navy type numbers mean

What type number would the Royal Navy give a modern cruiser?

Probably a Type 80-series project number, because the number encodes role while the completed ship could still be called a cruiser.

Royal Navy type numbers describe an escort's intended role rather than its displacement or formal class name. Type 20 numbers are associated with anti-submarine escorts, Type 30 with lighter surface combatants, Type 40 with air defence, and Type 80 with general-purpose ships that have air-defence capability. A modern cruiser could receive a Type 80 project number and still be commissioned as a cruiser. One suggested explanation links the system's origins to the many postwar refits and role changes applied to wartime destroyers, sloops, and frigates.