Speaking at a reception to mark World Mental Health Day, May is expected to say: "When I first became Prime Minister, I stood on the steps of Downing Street and pledged to fight the burning injustices in our society".
During the event, William aimed a good-natured ribbing at his wife after Middleton, who studied art history at the University of St. Andrews in Scotland, added a brushstroke to artist Dairo Vargas' painting.
For her appearance, Middleton wore a lavender Emilia Wickstead dress and carried a crocodile Aspinal of London handbag, accessorizing her ensemble with nude pumps, silver earrings and a matching necklace.
A dedicated minister for suicide prevention will be appointed as part of a landmark effort by the Prime Minister to tackle the UK's mental health crisis.
Kate, 36, who studied History of Art at St Andrews, where she first met her husband, laughed and took the brush from Mr Vargas, asking him: 'Where can you hide it?' Mr Vargas pointed to a shoulder area and Kate made her brushstroke - as William joked: 'It's nearly ruined the picture'.
Duchess Kate only returned to royal duties last week after taking maternity leave with little Prince Louis.
The duke and duchess were greeted by Health Secretary Matt Hancock
The pair attended the first Global Ministerial Mental Health Summit, an initiative that's been launched to raise awareness of mental health issues around the world.
They also took the time to meet with young people who have either had or are still dealing with mental health issues and met with representatives from a number of organisations running related campaigns and programs.
The Duchess chose a dress by Emilia Wickstead, wore previously during her 2017 royal tour of Germany.
Catherine - who also has children Prince George, five, and three-year-old Princess Charlotte - then praised the artist for his work.
The couple, along with Prince Harry, have been credited with helping break down the stigma surrounding mental health by encouraging open conversations about it.
Mental health issues signify disorders that affect mood, thinking and behaviour of an individual due to depression, anxiety, schizophrenia and even eating disorders and addictive behaviours.