The higher rate mobility component of DLA would normally only be awarded if a claimant is severely mentally impaired, as a result of a mental illness.
As (severe) anxiety and depression are ordinarily classed as mental health 'problems' as opposed to 'illness' (wrongly in my view), it would be very unlikely that the HRMC would be awarded in these circumstances, unless a claimant could satisfy section 73(3)(a)(b)(c) of the
Social Security Contributions and Benefits Act 1992.