It's not that people were having more babies during industrialization that caused the populations to grow as much as they did, it's because the babies started to live past infancy and people lived longer thanks to medical modernization.
Population growth has four (general) stages:
I: Birth and death rates are largely in equilibrium, with population only gradually increasing.
II: Death rate drops sharply, population boom ensues.
III: Birth rates begin to decline because of less need for so many babies
IV: Birth and Death rates are both much lower, and back in equilibrium. In the generation that makes the transition, you have a tonne of old people.