Ms Rantzen will call for the measure in a documentary to be broadcast on Sunday. The plan was criticised by teachers' unions.
The Panorama programme also features interviews with parents of a range of bullying victims, including those of Laura Rhodes from Neath in South Wales, who allegedly committed suicide in September.
Her parents claimed she had been bullied at her former school, Cefn Saeson.
The comprehensive was praised by inspectors last month for its outstanding care of its pupils.
Panorama: Why Bullies Win is on BBC1 on February 13 at 10.15pm