I did some other looking around and found the Civil Service issued guidance document: Best practice guidance on monitoring equality and diversity in employment (available here). Cornish is not mentioned once and searching the government website only finds one mention of Cornish minority status; the press release Cornish granted minority status within the UK.
I have today contacted Danny Alexander and Stephen Williams (who both triumphantly announced Cornish recognition in the run up to the European elections), to ask what is being done to make good on the promises to recognise the Cornish. To enquire why the government is not taking Cornish inclusion in the Framework Convention for the Protection of National Minorities seriously. Any answers I receive I will post here.