Why CVA-01 was likely to operate the E-2 Hawkeye

Would CVA-01 have used the British P.139B as its Gannet replacement, or the E-2 Hawkeye?

Probably the Hawkeye, because the small British requirement made an indigenous aircraft expensive and a shared NATO type offered scale and interoperability, especially if France adopted it too.

A British carrier force of only two or three ships would probably require roughly a dozen to fifteen airborne early-warning aircraft, too small a production run to absorb a bespoke programme easily. The much larger American Hawkeye fleet offered scale, while possible French adoption strengthened the political case for a common Western carrier aircraft. A shared type would also improve NATO carrier interoperability instead of leaving Britain with a tiny national fleet. A joint European commitment to P.139B might have changed the calculation, but cost and interoperability make Hawkeye the more likely choice for CVA-01.