My sister recently passed away and it is now going through a tribunal. Can the newspapers name her young children without permission?
I'm not able to give a full answer here I'm afraid. I haven't specifically researched this type of question before, and I think it would take me a couple of hours to produce a reasonable comprehensive and well-grounded answer. I have nonetheless done a little digging in relation to the data protection issues, and some of what I found may be of help.
There may also be relevant points and arguments in relation to the application of the right of privacy under the ECHR and certain common law rights, which I have not considered here.
In general terms, the processing of personal data for journalistic purposes is subject to wide-ranging exceptions from the specific provisions of the GDPR. Art 85 (https://gdpr-info.eu/art-85-gdpr/) provides:
(1) Member States shall by law reconcile the right to the protection of personal data pursuant to this Regulation with the right to freedom of expression and information, including processing for journalistic purposes and the purposes of academic, artistic or literary expression.
(2) For processing carried out for journalistic purposes or the purpose of academic artistic or literary expression, Member States shall provide for exemptions or derogations from Chapter II (principles), Chapter III (rights of the data subject), Chapter IV (controller and processor), Chapter V (transfer of personal data to third countries or international organisations), Chapter VI (independent supervisory authorities), Chapter VII (cooperation and consistency) and Chapter IX (specific data processing situations) if they are necessary to reconcile the right to the protection of personal data with the freedom of expression and information.
In the UK, the exemptions are set out in Part 5 to Schedule 2 to the Data Protection Act 2018 (http://www.legislation.gov.uk/ukpga/2018/12/schedule/2/enacted).
In summary, journalism is one of the "special purposes" under these provisions. The "listed GDPR provisions" (which cover various principles, rights and obligations) do not apply to the extent that the controller reasonably believes that the application of those provisions would be incompatible with the special purposes. In determining whether publication would be in the public interest the controller must take into account the special importance of the public interest in the freedom of expression and information. The controller must also have regard to certain codes of practice, including the Editor's Code of Practice.
I suggest you start by reviewing that document. It is available at: https://www.ipso.co.uk/editors-code-of-practice/
Sections 6 and 7 deal especially with children.