Surname Profiler here http://www.nationaltrustnames.org.uk/Surnames.aspx shows no results for Kirkuff. That means there were less than 100 by that name in Britain in 1998.

It could be Slavic, from Kirkoff, or most anything else. The only way to really know a surname ancestry is either the long slow process of tracing the paper trail back generation by generation, or perhaps---and just perhaps----by Y chromosome DNA. See www.ftdna.com for their FAQ on this.