Luckily the schools you worked in had nothing to hide, so they chose to show materials to parents who asked to see them.
Unfortunately, the Information Commissioner's Office has sided with a school that chose not to show materials to a parent who asked.
"In a landmark decision, the ICO backed the school's choice to keep the lesson and teacher's identity secret from parents, prioritising the commercial interest of a third party education provider over the public interest of parents to know what their children are taught. They have also prioritised the privacy of the teacher over safeguarding concerns."
This is despite the Dept of Education stating that "parents should be given every opportunity to understand the purpose and content of Relationships Education and RSE".
For up to date info about this case, which demonstrates that parents do not currently have a legal right to this information, there is a link in my post that you quoted. It is right under this text:
Transparency In Schools - FOI Appeal To Access Secret Lesson Plan
(I am not posting the link again because it is to a Crowdfunder. Whilst Mumsnet was kind enough to allow it to stand on that occasion, I do not want to push my luck by posting the link again.)
This is an interview with the mother, Clare Page, by barrister Dr Anna Loutfi about what happened when Clare asked to see the lessons taught at her daughter's school:
What's Being Taught In Our SCHOOLS? - The Bad Law Show - Clare Page