Lambeth and Southwark councils referred the matter to the secretary of state when they did not agree with local NHS proposals to reconfigure mental health crisis services.
South London and Maudsley foundation trust's proposals included closing the emergency clinic at the Maudsley Hospital.
The clinic is the only 24-hour self-referral service of its kind in the UK and has been open since the 1950s.
Lambeth and Southwark councils formed a joint health scrutiny committee which concluded that the changes were not in the interests of the local health service and that the matter could not be resolved locally.
But in a letter to the committee, Ms Hewitt said that closing the clinic was 'in line with the mental health national service framework and other departmental policy, and therefore in the interests of the local health service'.
Committee chair Angie Meader said: 'I think she's been very selective in the points we've raised that she's responded to. She's not looking at the whole - she's just looking at the words on paper rather than the reality of patients.'
Ms Meader said she was 'disappointed' but that the decision was 'not unexpected'. She added: 'The proposed closure of the emergency clinic has become a symbol of a [future] lean health service.'
She continued: 'When you lose one thing, it doesn't mean other things get better. It just means services are diminished.'
Lambeth council's legal department will now 'read the small print of the Local Government Act' to see if there are any future areas of action.
Local service users were set to stage a demonstration on Wednesday 24 January outside Southwark Town Hall.
The closure of the clinic will affect 18 jobs, but a trust spokeswoman said: 'We don't see any redundancies. There would be redeployment for staff affected.'