The Hague convention adoptions are recognised in the UK and the child will normally gain automatic British citizenship, provided one of the adoptive parents is habitually resident in the UK and is a British Citizen. The rules and process governing recognition of British citizenship status of the adopted child are however very complex. You should book a consultation for legal advice to verify whether adoption in question is recognised and whether the child really does qualify.
The Hague Conference has currently 82 Members: 81 States and 1 Regional Economic Integration Organisation. For the dates of membership, please consult the status table of the Statute of the Hague Conference.