That is fair enough. I would have no problem with my own family solicitor who acts on my behalf and on my instructions only, having a copy of such a personal and private document on file if need be. Some cowboy of a land lord, estate agent or auctioneer, who I know nothing about, and have known for all of 5 minutes doing the same thing? I don't think so !
I just heard back today from the estate agent who is handling the apt that I will be renting soon. All she needed was my bank info to verify that I have the capability to pay the rent by standing order, work references and previous rental history references. No other info or photo ID was needed. I am having a hard time seeing a circumstance where they would be needed, unless the personal circumstances of the tenant were very unorthodox or shady, and nothing that the OP has said so far indicates that that is the case.