As Kenya was a Colony it came under the jurisdiction of the Colonial Office, so the European public servants like prison officers would probably have been employed by the Colonial Office. This was merged into the Foreign and Commonwealth Office (1960s?). They have recently dispersed their library and records to a variety of places, including the National Archives, but if you google Foreign and Commonwealth Office Library there is a lot of information about what went where and, I understand, they still have a small unit which can give some information or point you in the right direction. Might be worth a look. You could also look at the South African records to see if you can find a birth for Jessie.