You asked
I was wondering if you have some statistics on the number of families with one or more parent with a mental illness in the UK for the year 2015-2016?
We said
Unfortunately, we do not collect data on the number of families with one or more parent with a mental illness in the UK.
I would suggest contacting Public Health England as they have a Mental Health Intelligence Network which may prove more useful.
https://www.gov.uk/government/organisations/public-health-england