Until the arrival of the Great Western Railway in Aylesbury in 1839 California was the name of a farm and related buildings that stood in the area. However with the arrival of the railway, cottages were constructed in the location of the farm to house railway workers and the area became known as the Hamlet of California.
By the early 1920s Aylesbury had grown such that it was necessary to start building houses on the site of Southcourt (the other side of California from Aylesbury), and so California and the associated farmlands that surrounded it became part of Aylesbury town. Eventually the farmlands themselves were built on, though the railway cottages that formed the hamlet remain.
Today the name California lives on in Aylesbury as the industrial buildings that were built on the farmlands next to the railway line are called the California Industrial Estate, and California hamlet is still marked on modern maps of Aylesbury.
The hamlet was probably named after California, USA, though its history goes back long before the State of California was known about by British people. The name of the original farm was therefore most likely changed to California at some point before 1839.