|Food vessel from child's grave Doune in Perthshire (National Museum of Scotland)|
"Food vessel" substitution is a distinct tradition in the late Insular Beaker Culture, although it was variously practiced both before and outside the Beaker Culture. Other continental Beaker cultures did incorporate other vessels into graves, but usually not as substitutions for Beakers and not of this heavy, flower pot style.
Because British Beaker Culture drew from several origins, its distribution is also not uniform. The Central European derived Wessex Culture wasn't really into food vessels and the earliest Beakers in both Ireland and Britain are not associated with food vessels. So food vessels are variously viewed as a late development, possibly a re-emergence of an older tradition and something preceding Collard Urns.
Food vessels have a strange origin because while they are similar to Middle Neolithic types within the region, they don't seem to have direct continuity at the local level. They do look like Peterborough Ware, but it would be something like Early Mississippian or Woodland Indian pottery suddenly becoming popular again. It's kind of hard to imagine how clunky pottery like this became a popular burial vessel.
FOOD VESSEL POTTERY FROM EARLY BRONZE AGE FUNERARY CONTEXTS IN NORTHERN ENGLAND: A TYPOLOGICAL AND CONTEXTUAL STUDY
NEIL C.A. WILKIN, 2013/2014 [Link]