Hi,
You linked to some BBC audio content. They also provide some written information which I have just copied-and-pasted below:
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Email-based age estimation
How it works
You provide your email address, and technology analyses other online services where it has been used - such as banking or utility providers - to estimate your age.
What are the privacy issues?
Verifymy are one of operators, and it told the BBC its research identified this as the method users would be most comfortable with.
Mr Lulham says the technology checks if an email has been used to interact with a range of websites such as financial institutions.
Verifymy said data could be kept for up to 28 days, but added it would often be less, would be encrypted, and no data would be shared with the website being accessed.
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[ Taken from https://www.bbc.co.uk/news/articles/ceq7ye3q2zwo ]
There is very little information about exactly what this "technology" actually is when they say "technology analyses other online services...." Apparently the algorithms involved are proprietary and no details are likely to be made available to the general public. It would be alarming if banking websites were just making a database of all the email addresses of their clients available to a service like "verifymy", however... they might be.....
There's some information available here: https://www.ofcom.org.uk/siteassets/resources/documents/consultations/category-1-10-weeks/284469-consultation-protecting-children-from-harms-online/responses/verifymy---white-paper.pdf?v=385741
That is supposed to have been a white paper submitted by verfiymy to OFCOM about their age estimation technology. I've scanned through it and would draw your attention to page 12 where there is flow chart style diagram of what the technology involves. In particular please note that the core workings of the process are described as follows...
The submitted email address is analysed using proprietary algorithms and external data sources. This includes reviewing sites such as.... finacial institutions, mortgage lenders or utility providers...
I can only understand the "external data sources" to mean that at least some financial websites are making some of their data available to verfiymy.
Anyway, that's all I've been able to find out so far.
Best Wishes.