Welcome to rootschat
Not an easy time to look for someone, there is of course the 1911 UK and the Irish census, the Irish census is free to search/view and you can download the image as well,so you can hope he was born in 1910 so he is on it http://www.census.nationalarchives.ie/search/
You could also check on the index http://www.freebmd.org.uk/
which covers England and Wales to see if there is a death at that time of a likely Glover
also check http://www.cwgc.org/
in case he died during the War
Just a thought: You do have your mothers long birth certificate as the short one will not show parents.
It is difficult I have on single parent in one of my lines, who's mother was also a single parent and both women worked to support their own family so no records such as court, parish for financial help and have found it impossible to find either father...... maybe your mothers baptism record may have fathers name written.
Can't think of anything else you could look at but sure someone will have some more ideas
Leicestershire: Chamberlain, Dakin, Wilkinson, Moss, Cook, Welland, Dobson, Roper,Palfreman, Squires, Hames, Goddard, Topliss, Twells,Bacon.
Northamps: Sykes, Harris, Rice, Knowles.
Rutland: Clements, Dalby, Osbourne, Durance, Smith, Christian, Royce, Richardson, Dewey, Newbold,Cox, Chamberlaine.
Durham/Yorks: Woodend, Watson.
Suffolk/Norfolk: Groom, Coleman, Kemp, Barnard, Alden.
Lincolnshire: Clements, Woodend.