Why not just leave this with our current FM company?

Most FM providers are built around reactive works, with compliance bolted on as one line in a schedule. ICM designs the whole FM package around compliance: planned works are scheduled around keeping the record valid, and reactive tasks are prioritised by urgency and attended promptly, never queued behind compliance work. If compliance is a by-product of your FM contract, it is the first thing to slip when the contract is busy.