The phrase "went into labour" is correct and may be used in written English.
Example: When the time came, Sarah went into labour and welcomed her healthy baby boy into the world.
Cerys Matthews went into labour during a Stereophonics gig (4).
She knelt at his grave and promptly went into labour.
He rushed back from London to his home yesterday as his wife went into labour.
Masooma Hezara, 23, from Afghanistan went into labour in September 36 weeks into her pregnancy.
The day that she went into labour she heard it had been accepted for publication.
One was a pregnant woman who went into labour after being transferred to an MSF boat.
"The guards pushed me around, and after a few days I went into labour.
When Elle went into labour, she informed the hospital, as is routine in a home birth.
We played the album in the hospital when I went into labour.
Twenty minutes after the expectant mother went into labour, the police were knocking at the door.
On the big day, though, Helen went into labour at around 7am, just as the team's shifts were changing.
