No idea about pensions, sorry!
Using the site I mentioned above (not complete but pretty good coverage) there are 2 Greer children with mother's maiden name Bedwell:
Sep 1912 Dover 2a 2123
Robert Greer
Mar 1914 Woolwich 1d 2251
Margaret R Greer
You can't be sure the John Greer who married in 1912 is your John Greer unless you order the marriage cert to check that his age/occupation/father's name are correct
