Jacko et al,
The most recent action where carriers were absolutely essential was post 9/11 action in Afghanistan. Apart from B2s from the US (on round trips) there was no other way of delivering ordnance on Afghan soil than from aircraft carriers. All air combat power was delivered from the CVNs. No nation would offer combat support to the UK or US. ILLUSTRIOUS also launched ops into Afghan at this time.
The other action where flat tops were used because the shore facility failed was the assault on the Al Faw which ended up being launched from OCEAN and ARK ROYAL.
The final point is that the UK no longer has sufficient strategic airlift to deploy real combat air power into a theatre of operations and be effective on day one - and then day 2,3, 4 etc. CVF is the only real route for the UK and the Government and policy makers know it.