There were two John Radcliffe births registered in 1860:
Surname First name(s) District Vol Page
Births Sep 1860
RATCLIFF John James Liverpool 8b 183

Births Dec 1860
RATCLIFFFE John Liverpool 8b 195

If it was the first one you checked, perhaps check this other one as well?

There was also:
Births Dec 1857
Ratcliffe John Liverpool 8b 158

If you want to find who his mother was you may need to check a few!

Sue