This is a question that has been specifically determined by the House of Bishops.
You will still need to do the Church of England training for the role you are in.
The official answer can be found in the ‘Safeguarding Training and Development Practice Guidance‘ published by the Archbishops Council.
This is a quote from the practice guidance that explains the decision:
No accreditation is given against the core safeguarding training modules for prior learning that has not been provided by the Church of England framework.
This is due to church core safeguarding training modules situating safeguarding practice within the unique context of the church and providing participants with the opportunity to relate their learning to their faith.