It is clear that the British (was about to say UK, but that is not PC) armed services are vastly experienced, but completely out of scale with current military realities.
Imho, the British military should best be compared to the US Marine Corps, they are both roughly the same size and serve largely as overseas intervention forces.
That does suggest that if the USMC can maintain an integral air force with no more than unit patches, so could Britain.
What is of course missed is that the US Marines do get access to the whole doctrine, design, develop, produce and support bureaucracy of the rest of the US military.
The British equivalent of this is presumably in Whitehall, invisible to budget cutters, even though that is where most of the money goes astray.
To illustrate, Space X provided government launch services for about a third the cost of the United Launch Alliance, the previous monopolist supplier.
Yet the USLA books were fully compliant with the lowest cost, best price requirements of the Defense Contracts Audit Agency....