In the modern era, Carriers require a fast, capable picket line of Aegis destroyers...nuke subs...and back-up carriers.
Or, they must be relegated to being part of a US Navy Carrier Battle Group.
I don't believe Britain has sufficient surface and sub-surface assets to protect these ships operating independently. I would like to be wrong, but don't think I am.
In addition, they have been integrated into the US Navy's CSG defense program:
Their Astute SSNs are on par with our Virginia class too.
Problem is, they only have about sixe of each.
Probably enough to provide two Type 45s and one Astute for any one of their carriers deployed.