Asked and answered here: https://www.quora.com/When-renewing-a-UK-passport-is-it-unnecessary-to-disclose-other-foreign-passports-dual-nationality-to-the-UK-Passport-Agency
Reviewing the documents supplied under the FOIA, the most appropriate part of the documentation seems to be this:
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.
In your case, since your children were born abroad, there is an additional relevant section:
Requesting foreign passports when considering passport
applications for those born abroad
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.
