The Senate has passed a motion calling on the Australian Vaccination Network (AVN) to disband and cease its campaign against vaccines.

The motion, put forward by Greens Senator Richard Di Natale, notes the low vaccination rates in parts of Australia and the threat that poses to the health of children.

The motion says the AVN should cease its harmful and unscientific scare campaign against vaccines.

Senator Di Natale says the Senate has sent a clear and strong message to those peddling lies that "they should pack up and go home".

It comes after the New South Wales Fair Trading Department ordered the AVN to change its name.

It claims to be a lobby and support group that promotes health choices, but the department says that is misleading because it is, in fact, an anti-vaccination group.

The AVN actively promotes the link between vaccination and autism, a theory that was debunked by the medical world 20 years ago.

The AVN is resisting the name change order in court.