Perguntado e respondido aqui: link
Revisando os documentos fornecidos sob o FOIA, a parte mais apropriada da documentação parece ser esta:
The Royal Prerogative provides that Passports are issued when the Home Secretary is satisfied as to: (i) the identity of an applicant; and (ii) the British nationality of applicants, in accordance with relevant nationality legislation; and (iii) there being no other reasons (as set out below) for refusing a passport. IPS may make any checks necessary to ensure that the applicant is entitled to a British passport. The requirement to submit an uncancelled passports relates to any uncancelled passport, British or otherwise. The document is required to support identity and nationality checks. It is also required to ensure that any British passport issued is compatible with the biographical and photographic details contained in an existing passport.
No seu caso, como seus filhos nasceram no exterior, há uma seção adicional relevante:
Solicitando passaportes estrangeiros ao considerar o passaporte aplicações para aqueles nascidos no exterior
Section 03 of the passport application form asks "Has the person named at section 02 had ANY sort of passport, British or otherwise, or been included in any before?" It then states "All such uncancelled passport(s) must be submitted with the application." Requesting sight of any passport currently held establishes that an applicant who was born abroad is currently in the UK. It also provides additional evidence that can assist in determining identity, and entitlement in descent claims.