I just received this email from the archivist at Worcester Cathedral. Emphasis (on the directions how to get to the library) are mine!
Dear Miss Smith,
Thank you for your enquiry regarding coming to look at manuscripts F.32 and F.44. I have checked the diary and it will be possible for you to come on the days you mention. The door and intercom for the library is located in the south west corner of the nave behind the Victorian font. The library is reached by a medieval spiral staircase of 39 steps. If you have any further questions just let me know.
With best wishes,
Yours Sincerely,
Librarian/ archivist.
I found a picture. Can you see the door and the intercom button?

