You need to work backwards step by step.
From Patrick Henry A Collins' birth certificate you will have his mother's maiden name. In fact that can also be found in the GRO index for Sep qtr 1907, and it's Sullivan.
Next look for a marriage of Henry Collins and Elizabeth Matilda Sullivan, which according to FreeBMD was in the Stepney district in Jun qtr 1901. This marriage certificate should give the names of their fathers.
(This method isn't entirely foolproof, since if Elizabeth Matilda Sullivan had been married before, the maiden name on PHAC's birth certificate wouldn't match the one she married Henry with.)
As well as looking at births, marriages and deaths, try to find your folk in censuses. You should be able to find your grandfather and his parents in 1911, and with the parents' ages and places of birth you may be able to find them in earlier censuses with their own parents.
Another caveat: if they go back to Ireland, things can get a bit harder, but do what you can in England first and then ask again about how to track them in Ireland.
