They say profits would flow in part to the Israeli oil and gas company Delek Group, which the UN human rights commissioner accuses of "supporting the maintenance and existence" of illegal settlements in the West Bank.
Legal advice commissioned by the environmental group Uplift, says the link with Delek means the UK government risks breaching the Geneva Conventions if it gives drilling at Rosebank the green light.
Delek did not respond to a request for comment.
The UK government said it could not comment on individual projects.
Uplift's legal advice refers to potential breaches of Article 49 and Article 53 of the Geneva Conventions, which relate to occupation, deportation and the destruction of property.
It also alleges that Delek's activities could be regarded as "ancillary" to war crimes and crimes against humanity under Section 51 of the International Criminal Court (ICC) Act 2001.