Maybe there is some mechanism available..?

As far as I am aware, the only information that an organisation is obligated to provide is one's Personal Information following a Subject Access Request under GDPR. (I will leave it to others with a better understanding of GDPR to expand on this or correct me if I am wrong.)

From reading books...

If you are proposing civil action as a "Litigant in Person" (i.e. without a lawyer), then you should consider reading the Civil Procedure Rules, especially Part 31 - Disclosure.*

Also worth reading is the Handbook for Litigants in Person written by the Judiciary as part of their general Advice for Litigants in Person.

*Just to clarify; the term and processes of "Discovery" no longer exist in the UK, being replaced with "Disclosure" by Lord Woolf' Reforms in 1999.

Maybe there is some mechanism available..?

As far as I am aware, the only information that an organisation is obligated to provide is one's Personal Information following a Subject Access Request under GDPR. (I will leave it to others with a better understanding of GDPR to expand on this or correct me if I am wrong.)

My situation is civil law and the main intention is to obtain factual evidence...

If you are proposing civil action as a "Litigant in Person" (i.e. without a lawyer), then you should consider reading the Civil Procedure Rules, especially Part 31 - Disclosure.*

Also worth reading is the Handbook for Litigants in Person written by the Judiciary as part of their general Advice for Litigants in Person.

*Just to clarify; the term and processes of "Discovery" no longer exist in the UK, being replaced with "Disclosure" by Lord Woolf' Reforms in 1999.