Two young girls, aged 23 and 15, had reportedly fled their home in Baghpat district in Uttar Pardesh after village elders allegedly ordered that they be stripped naked and paraded publicly after their brother eloped with a married woman.
The sisters and their father have now appealed to the Supreme Court for protection.
Nadhim Zahawi, a Conservative MP of the UK foreign affairs select committee, condemned the ruling as "disgusting" and urged the UK Foreign Office to intervene.
Hilary Benn, the shadow foreign secretary, added: "I urge Philip Hammond (UK Secretary of State for Foreign and Commonwealth Affairs) to make immediate representations to the Indian authorities for action to be taken to protect the two sisters."
A spokesperson for the Foreign Office said: "We are aware of the particular concerns around violence against women and girls in India and are committed to working with the Indian government on this important issue.