Why the RAF needed the E-3 Sentry rather than a land-based Hawkeye

Why did the RAF not adopt a land-based E-2 Hawkeye for airborne early warning?

Because the E-3 Sentry's larger crew and command capacity better matched theater-wide land-based operations, while the Hawkeye was optimized for a carrier group.

The Hawkeye is optimized to fit a carrier and manage the air battle around a task group with a pilot, copilot, and small operator team. A land-based Royal Air Force aircraft did not need those deck constraints. The E-3 Sentry could carry a flight crew and a much larger mission staff, allowing it to coordinate aircraft from multiple bases across the European theater. A later discussion of the source material describes the Hawkeye comparison as an option that officials had to evaluate and reject, not evidence of a serious plan to replace the Sentry with a carrier aircraft.