Archbishop Cranmer began work on his Book of Common Prayer at the Palace. It is believed that he finished this work before he left. A background to the Book by Rev’d Canon Dr Judith Maltby can be found on YouTube.
The Book of Common Prayer went through several revisions in the years after it was first written. You can read the various versions in:
Cummings, B. (2013) The Book of Common Prayer The Texts of 1549, 1559, and 1662. OUP Oxford. ISBN:-13: 978-0199645206