Earlier that month, Mann contacted police claiming she had received abusive text messages which she said had been sent by Mrs Page.
She had in fact sent them to herself.
She then used the same phone to make the bomb hoax call 17 days later.
Appearing at Wood Green Crown Court today Mann, 43, of Uphill Road, London NW7, admitted attempting to pervert the course of public justice three times over a three-week period in July 2013.
Outside the court Mrs Page described her relief at the outcome.
“I was sure she would never admit it. I burst into tears when she said she was guilty,” she said.
Last week at Harrow Crown Court, Mann admitted a separate charge of perverting the course of public justice.
She will be sentenced for both offences in August.