“Years of undercover investigations have revealed the systemic failures of the RSPCA Assured scheme. The RSPCA must be bold and take decisive action now,” she added.
She also called on Mr Packham to step down from his role as president.
But a joint statement by Mr Packham and vice-president Caroline Lucas said the pair would take no action themselves until the results of a “full and independent review” they had demanded were published.
They said it would be “dishonourable and disingenuous” to do so until they had seen the findings.
The pair added that they “understand, sympathise with and respect” Sir Brian’s decision to resign.
They also pointed to concerns at the heart of the row – whether the RSPCA should be involved with the farming of animals for food at all.
“The only way to completely stop the abuse of ‘farm’ animals is to stop farming animals”, they added.
The RSPCA Assured scheme – originally known as Freedom Food – was launched 30 years ago and covers meat, fish, eggs and dairy. Certified farms have to follow strict welfare standards that are set out by RSPCA welfare scientists and are higher than is legally required in the UK.
An RSPCA spokeswoman said it respects Sir Brian’s “views and understands his decision” before adding: “His ongoing and devoted work campaigning on issues such as the badger cull and hunting have been invaluable for all animals and we look forward to speaking up on these issues with him in the future.”
The spokeswoman also called farming “hard, and farmed animal welfare is even harder”.
But, she added, the RSPCA wanted to “give our supporters, partners and the public confidence that RSPCA Assured is consistently delivering better welfare than standard farming practices.
“So, we launched an independent review of RSPCA Assured, which has been carried out over several months, including unannounced visits to more than 200 members of the scheme.
“Once we have analysed our findings, we will take any robust action necessary.”