Birth certificate is OK if the person checks out as a british national and the identification matches that in one of the the docs listeds (most are letters from from trusted individuals and or institutions asserting the supporting the right to rent AS BRITISH CITIZENS)
In this case you don’t need photo id - if the person checks out as British with the two documents
Interestingly though, I’ve only ever had one applicant that didn’t have photo ID. They never turned up to the viewing anyway, despite me asking them to bring the other forms of ID you listed and sending them that very link in fact!
Personally, I’m happier with photo ID as it enables me right from the start to know that the person I’m talking to is in fact who they say they are.