The question asks which judgment contains Lord Wright's observation that the incalculable value of habeas corpus lies in enabling the immediate determination of an applicant's freedom. Matching the quote's subject matter and era against each case narrows this down.
- Attorney General for New South Wales v. Trethowan, (1932) AC 526: This case concerns the legislative procedure required to alter a state constitution, specifically the manner and form of legislation, and has nothing to do with the personal liberty focus of habeas corpus. It does not match the subject of the quoted observation.
- Attorney General for Hong Kong v. Ng Yuen Shiu, (1983) 2 AC 629: This is a well-known administrative law case establishing the doctrine of legitimate expectation, decided decades after Lord Wright's era and on a different legal question entirely, so it cannot be the source of this habeas corpus remark.
- Bugdaycay v. Secretary of State for the Home Department, (1987) AC 514: This case deals with judicial review in the immigration and asylum context, applying anxious scrutiny where fundamental rights like life are at stake. While it touches on liberty concerns, it is a later case decided in a different context from Lord Wright's wartime-era observation.
- Greene v. Secretary of State for Home Affairs, (1942) AC 284: This case arose from wartime detention under the Defence (General) Regulations, 1939, and directly engaged with the role and value of habeas corpus as a check on executive detention. Lord Wright's remark about the immediate determination of freedom fits squarely within a judgment examining the writ's core purpose in exactly this setting.
Matching the wartime detention context and the specific focus on habeas corpus as a guardian of personal liberty points to only one of the four cases, since the others deal with legislative procedure, legitimate expectation, or a later immigration context.
Therefore, the correct answer is Greene v. Secretary of State for Home Affairs (1942) AC 284.