The pair join the previously announced cast members Olivia Colman and Harry Potter star Katie Leung.
The gritty four-part series follows the stories of four unconnected people whose lives intertwine in a story of modern-day survival.
Winstone will play nightclub stripper Tara, whose boyfriend is murdered. She discovers the news from his secret partner.
Lennie James will star as a recovering heroin addict, who his trying to rebuild his life in order to reconnect with his daughter.
Commissioning editor Sophie Gardiner said of the series: "Channel 4 has a proud history of developing new drama talent both on and off screen and we are delighted to be continuing in that tradition with Run, a beautifully authored and original series about a strand of British life rarely seen on our screens."
Each episode will focus on a different character, and will be directed by BAFTA-nominated Skins and Being Human helmer Chris Martin.
Lennie James recently spoke to Digital Spy about his recent role in BBC Two thriller Line of Duty.