G
First, I must correct you it is not "serious" but rather "severely", the difference is important.
Whilst I am not aware of a specific definition for "severely mentally impaired" I think you should take it as those suffering the most disabling of mental illnesses.
To qualify under this criteria you have the support of your GP or a doctor able to sign such a certificate.
You can apply directly to your Local Authority, there are other criteria that will offer a discount, see
www.gov.uk/apply-for-council-tax-discount/west-northamptonshire Gordon