Our organisation is still using Windows 7 or Windows Server 2008 R2 – is this Cyber Essentials compliant?

Normally no, this would be regarded as an instant fail as the software is unsupported (both went End of Life 14/01/2020).
In circumstances where your organisation has paid for Extended Security Updates (ESU) from Microsoft for every device that is unsupported, this will be considered permissable as technically the software is supported.