Using the 1881 census for England & Wales as a basis, the five variant names are distributed as follows:
Akehurst - 66.0% - mainly found in East Sussex
Akhurst - 26.4% - mainly found in southern and western Kent
Ackhurst - 5.4% - found almost equally Kent and Sussex
Ackehurst - 0.8% - originated from one family in Etchingham
Akurst - 0.8% - mainly found in Kent
Over the span of the censuses from 1841-1901, the relative frequency of the Akehurst and Akhurst names have remained static, the Ackhurst and Akurst names are in slow decline, and the Ackehurst name has appeared.