Hi Elaine, I had a little more time this morning & have checked the NBI Barnsley listings & the only Barnsley listing on the disc is for St Mary's Church. Barnsley Cemetery on Cemetery Rd which would be likely to be where your William was buried was not included in the NBI.
If you have not already done so it may be worthwhile contacting the Friends of Barnsley Cemetery at http://friendsofbarnsleycemetery.webs.com/contactus.htm
Also Barnsley Council Bereavement Services at bereavementservices@barnsley.gov.uk
Best of luck, John
Barnsley Cemetery
There are 6 burial records for the surname Mayo
William Mayo buried 13 November 1915 age 53 / 23 Henshall Street
Annie Elizabeth Mayo buried 2 May 1942 age 72 / 23 Henshall Street
William Mayo buried 7 December 1962 age 62 / Beckett Hospital /23 Hensall Street.
All buried in the same grave section H plot 634
Irene Mayo buried 1 March 1941 age 3 month St Helens Hospital / 17 Ebor Street
Gladys May Mayo buried 7 April 1970 age 59 Beckett Hospital / 2 Yews Place Kendray
Arthur Mayo buried 25 February 1983 age 76 Mount Vernon Hospital
All buried in the same grave section 9 plot 443