French ambassador Sylvie Bermann, 62, argues that the planned basement next to her diplomatic home in London would infringe their diplomatic rights under the 1961 Vienna Convention.
India, Russia, Japan, Saudi Arabia and Lebanon have backed Bermann's protest against the proposed four-storey basement in Kensington Palace Gardens, London's most expensive address.
The diplomats, who all live on the same exclusive west London street, have written to their freeholder, the Crown Estate, urging it to "protect the integrity of our residences."
The diplomats refer to Article 22 of the Vienna Convention, which obliges host states to protect diplomats' premises from "intrusion or damage" and prevent "disturbances of the peace of the mission or impairment of its dignity," the Sunday Times reported.
India's backing is likely to have come from recently retired Indian high commissioner to the UK Ranjan Mathai.
Bermann, who became ambassador in August 2014, lives in a 19th-century mansion which was previously the residence of the 10th Duke of Marlborough.
It has been rented by the French government since 1946.
Hunt, 62, and his wife Lois, 60, a former nurse, bought the former Soviet embassy, a grade II-listed eight-bedroom mansion next door, for almost 16 million pound in 2005.
"The scale of the underground work planned is such that, were work to proceed, it could jeopardise diplomatic activities," said a spokesperson for the French embassy.