Another PM shows an Alien Registration document; I have no experience with these but do not think they show British citizenship.
Is anyone familiar with these documents and can explain what they are for?
Yes I am familiar with Aliens Registration documents. When a foreign national was admitted to the UK, the immigration officer could require them to register with the police so that their whereabouts were known. It was a requirement introduced at the outset of WW1, to keep a track of “enemy aliens” etc, and was used to locate them when internment was introduced, and to monitor those allowed to remain at liberty. But after the war it was continued to ensure the authorities knew where most foreign nationals lived, in the event of needing to trace them urgently. It only applied to “aliens” ie people who were not British Citizens or Commonwealth citizens.
A person with an Aliens Registration Certificate had to report changes of address to the police, as well as changes of employer (for those with permission to work).
The requirement to register with the police was normally discontinued once someone acquired permanent residence (green card status in US terms), and certainly didn’t apply to someone who had acquired British Citizenship. So having an Aliens Registration card meant you definitely were not British (at that time anyway).
Police registration for foreign nationals is still in use today, though not quite as widely as in the 1920s.