Extra training for teachers, an extra £15m for community care, and online self-checks were among measures announced by the PM on Monday.
Mental health experts said more funding was needed to improve services.
Mrs May's speech comes as she outlined her plans to use the state to create a "shared society".
She promised to "transform" attitudes to mental health problems as part of an event at the Charity Commission.
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The government says that, at any time, one in four people has a mental disorder, with an annual cost of £105bn, and that young people are affected disproportionately.
In the speech, Mrs May announced:
Every secondary school to be offered mental health first aid training
Trials on strengthening links between schools and NHS specialist staff, including a review of children and adolescent services across the country, led by the Care Quality Commission
By 2021, no child will be sent away from their local area to receive treatment for mental health issues.
Full speach http://www.bbc.co.uk/news/uk-politics-38548567