One complicating factor is that if, before the children's births, OP:

• resided in Australia,

• had "a clear and fixed intention of making their permanent home or indefinite residence in" Australia, such as:

• • bank accounts, voter registration, burial location intentions, few long visits to the UK, etc

• https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/1117564/Legitimacy_and_domicile_guidance__V3_FOR_GOV.UK_publication_.pdf#page=18 (pages 18-20)

then OP may have been considered "domiciled" in Australia at the time of the births.

Since 1984, Australian law has had no distinction between children born to married parents and those born to unmarried parents --

• https://webarchive.nationalarchives.gov.uk/ukgwa/20220303054130/https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/118568/legitimation-and-domicile.pdf#page=14 (pages 14-15).

Thus, if OP was considered domiciled in Australia at the time, then OP's children would have been considered born "legitimate" and would have acquired British citizenship at birth.

A child will be considered legitimate, for the purposes of the British nationality law: ...

...

• by the laws of the country where their father was domiciled at the time of the birth, regardless of whether their parents were married or not

• https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/1117564/Legitimacy_and_domicile_guidance__V3_FOR_GOV.UK_publication_.pdf#page=6 (page 6)

In such a case, the children could simply apply directly for British passports, without a Form UKF registration for citizenship required.

/u/RedDirtNurse