On the trail of my husband's Slatter ancestors from Marylebone and Oxfordshire, I e-mailed the Slatter genealogist in Oxfordshire to ask whether his family and hubby's family are related. Twelve hours later, this wonderful gentleman wrote back to say no relation...but he did a lookup for me and found more info about John Slatter in Oxfordshire!
John Slatter, college cook, of Oxford (St. Ebbe parish), was married by license to Sarah Harris of same parish on 1 May 1832.
On the baptismal records for John & Sarah's first three children, John's occupation is shown as "college cook," then "cook at ch. ch." (probably Christ Church), then "cook at ch. ch college."
In the 1841 UK Census, John Slatter (Senior) was shown as a cook, living in Banbury parish, Oxfordshire.
By 1859, when John Slatter Jr gets married, John Slatter Sr is listed on the marriage license as "deceased" father of the groom, along with his occupation, which is "cook."
Next steps: Find out more about Sarah Harris and check the records of the Oxfordshire Family History Society, as recommended by the Slatter genealogist.