William Jefferies wrote his autobiography in 1886.   This included transcriptions of two journals that he kept from 1858 to 1862 detailing his work as a missionary in England and his emigration to the United States of America.   Also included in the book were some miscellaneous notes and additions made by his two of his sons.  

In the 1950's, William Jefferies son, Murray Jefferies, transcribed this book into a typed format, and donated the original to the Historian's Office of the Church of Jesus Christ of Latter-day Saints.   Several copies of this transcription were made and distributed to family members.  

As to where the journal is now located, I received the following email:

Dear Mr. Jefferies:

The journal of William Jefferies is at the LDS Church Archives and is viewable to you as a descendant.   We are on the second floor of the east wing of the Church Office Building at 50 East North Temple, Salt Lake City, and we are open Monday through Friday from 8:30 to 4:15.   We originally had it cataloged under the name of William Jeffries.   Thanks to your inquiry we will change it.   If when you come, it has not been changed yet, also check under the name of Jeffries.  

All the best,
Ron Watt
Archivist, Sr.