Step 1: Understand the question.
We must find the case where it was held that the rules of natural justice are not limited to the narrow idea of quasi-judicial functions.
Step 2: Know what natural justice means.
Natural justice means fairness, openness, and no bias in decisions. Earlier, courts applied it only to quasi-judicial actions, not to plain administrative actions.
Step 3: Recall the facts of the key case.
In the selection of officers for the Indian Forest Service, one member of the Selection Board was himself a candidate. Though he stepped aside for his own case, he took part in judging other candidates. This raised a serious bias problem.
Step 4: Recall the ruling.
The Supreme Court said the line between administrative and quasi-judicial power is thin and is fading. It held that whenever a decision affects a person's rights or interests, natural justice should apply, even to administrative actions.
Step 5: Check the other options.
Conway v. Rimmer dealt with public interest immunity. Ridge v. Baldwin expanded natural justice in England but is not this quoted case. Maradana Mosque Trustees concerned administrative discretion but not this principle.
Step 6: Reach the answer.
The case that laid down this principle in India is A.K. Kraipak v. Union of India.
\[ \boxed{\text{A.K. Kraipak v. Union of India AIR 1970 SC 150}} \]