The 1891 census entry shows he was John P Burke and reveals his mother's maiden name (Conroy) so we can confidently identify the birth. It was probably March 1889 to beat the census deadline but overflow into the next quarter.
Household Role Gender Age Birthplace
Ann Conroy Head F 53 Ireland
Mary Burke Daughter F 23 Lancashire, England
William Burke Son In Law M 23 Lancashire, England
John P Burke M 2 Lancashire, England
James Burke M 0 Lancashire, England
"England and Wales Census, 1891," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:Q518-JW2 : 15 October 2015), John P Burke in household of Ann Conroy, Burnley, Lancashire, England; from "1891 England, Scotland and Wales census," database and images, findmypast (http://www.findmypast.com : n.d.); citing PRO RG 12, Lancashire county, subdistrict, The National Archives of the UK, Kew, Surrey
Name John Patrick Burke
Event Type Birth Registration
Registration Quarter Apr-May-Jun
Registration Year 1889
Registration District Burnley
County Lancashire
"England and Wales Birth Registration Index, 1837-2008," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:2XYC-9L4 : 1 October 2014), John Patrick Burke, 1889; from "England & Wales Births, 1837-2006," database, findmypast (http://www.findmypast.com : 2012); citing Birth Registration, Burnley, Lancashire, England, citing General Register Office, Southport, England
Now searching for John P Burke deaths of the right age there's only one match - Q1 1968 aged 78 in the slightly surprising location of Cardiff. Of course it's possible the death was recorded abroad or without the initial but this is a strong candidate.
http://www.freebmd.org.uk/cgi/information.pl?cite=wyYH4Uwus%2ByVzKywQ74fww&scan=1