The MOU is not legally binding but it represents a published approach to joint working which has been signed-off by both departments and formalises the approach taken on regulatory compliance issues.
The MOU emphasises that:
Also worthy of note is that the DfE has agreed extensive input into the Commission's regulatory process in respect of charities of which the DfE is principal regulator, including inviting the Commission to exercise its extensive regulatory powers. Although the DfE is not principal regulator of charitable independent schools, this level of involvement or influence may set the scene for the less formal arrangement where each "may identify potentially serious concerns" and "agree at the earliest opportunity a case strategy" in respect of independent schools.
You should continue to be aware that information about your school is likely to be shared between the DfE and the Charity Commission, including in relation to regulatory compliance and public benefit issues. This could lead to both departments working together on regulatory concerns and the enforcement powers of both regulators being used.