For the purposes of the Equality Act 2010 does a mental illness have to be clinically well recognised?

No. While the Disability Discrimination Act 1995 used to state that a mental impairment included an impairment arising from or consisting of a mental illness only if the illness was clinically well recognised, this provision was removed with effect from 5 December 2005 and is not included in the Equality Act 2010, which replaced the Disability Discrimination Act 1995 as of 1 October 2010.