Not Vital Interests.
"As for actual data processing, Article 6 provides for the lawful processing of data where "processing is necessary in order to protect the vital interests of the data subject or of another natural person"."
On a technical note re. the article Article 6, Para(1(c)) does set out the use of Vital Interests however this needs to be read in conjunction with the relevant recital, in this case Recital 46.
https://gdpr-info.eu/art-6-gdpr/
https://gdpr-info.eu/recitals/no-46/
This clarifies that Vital Interests should only be used where no other Legitimate Basis can be relied on and processing " is necessary to protect an interest which is essential for the life of the data subject or that of another natural person" such as "humanitarian purposes, including for monitoring epidemics and their spread or in situations of humanitarian emergencies, in particular in situations of natural and man-made disasters."
The intent for Vital Interests is that it should only be used in life saving situations where no other form of consent or other basis is available. In this case that would be difficult to prove.
Article 5(e) is the applicable reference here as you point out.
https://gdpr-info.eu/art-5-gdpr/
"Kept in a form which permits identification of data subjects for no longer than is necessary for the purposes for which the personal data are processed; "
It also includes archiving in the public interest, scientific, historical or statistical research.
Since the purposes for which is was collected was to prove legitimate and lawful arrival in the UK for the data subjects an their dependants then keeping records for 75 Years or longer would be perfectly reasonable.