I found this page, which is basically a guideline for their staff. If I were you I would get in contact with your nearest British Consul and explain the situation. Considering your age and need for the passport to get a Thai visa, I can't see why they would be unable to process everything, maybe with an interview with the Consul or someone at the embassy.
https://www.gov.uk/government/publications/supporting-documents-not-available/supporting-documents-not-available-accessible