The Integrated Communities Innovation Fund, aims to bring together people across different backgrounds, to help them to benefit from "full participation in society", according to the Ministry of Housing, Communities and Local Government (MHCLG).
Luton Tigers, an organisation protecting young people from radicalisation, extremism and racism, is among the
The Tigers will hold an inter-school sports programme involving children competing with and against pupils from other schools.
Poetry, art, dance and drama workshops will also explore what pupils have in common as well as their differences.
Another project to received a cash boost is the Youth Sport Trust, which is addressing school segregation in Birmingham.
It will bring together 22 schools with different levels of disadvantage and diversity to help them integrate through sporting activity.
Planned activities include inspirational assemblies, sports events and volunteer training, culminating in a sporting festival.
Others to receive funding include the Behavioural Insights Team which is running two projects: one delivered by UKActive through its UK-wide physical activity camps during the summer holidays.
The second project aims to develop a new evidence-based curriculum for PSHE classes in 15 schools across Birmingham and Coventry.
The MHCLG fund, which delivers projects in partnership with Sport England, engages 70,000 people with activities in schools, community and leisure centres, and works collaboratively with businesses, councils and housing associations.
Communities minister Lord Nick Bourne said too many people were still "locked out of the benefits that come with full participation in society".
"To tackle the root causes of poor integration we need to bring together people from all backgrounds and from all parts of society, from business leaders to grassroots charities," he said.
The government will fund 14 projects across the UK while Sport England has committed around £270,000 to fund two projects in Birmingham and Brighton.
Tim Hollingsworth, chief executive of Sport England, said the projects would help people feel more connected to their communities and to society as a whole.
"Not only does taking part in sport and physical activity have powerful mental and physical health benefits, it can help people develop new skills and bring them together in a shared experience," he said.
The new projects support the government's ongoing work to tackle the causes of poor integration which includes working with five integration areas across England: Blackburn with Darwen, Bradford, Peterborough, Walsall and Waltham Forest, all of which have produced their own integration plans.
The five councils were chosen in 2018 as part of the government's integrated communities strategy which will see £50m invested in schemes to improve community relations over a two-year period.