The 1,2,3 campaign - launched by the charity Beating Bowel Cancer and fronted by TV doctor Chris Steele - urges people to learn three simple steps that could save their life.
It includes a short film showing people how to complete the faecal occult blood (FOB) test, which is sent to all men and women between the ages of 60 and 75 in England to be completed at home.
Screening is also available to people aged 60 to 69 in Wales; and those between the ages of 50 and 75 in Scotland.
The test requires a small sample of bowel motions to be collected on a test card on three separate days. The card is then returned to the screening centre by post and analysed for tiny amounts of blood, which could indicate a need for further investigation.
It is hoped that the film, which can be viewed on the campaign website, will help to boost participation rates and reduce the number of deaths from bowel cancer - the UK's second leading cause of cancer death.
Ed Yong, Cancer Research UK's head of health information, said: "Bowel screening is one of our best weapons in the fight against bowel cancer with the potential to save thousands of lives each year. We know that people from poorer backgrounds are less likely than richer people to accept their bowel screening invitations. We urge all men and women in the eligible age groups to seize the opportunity for their free bowel screening tests."
Professor Julietta Patnick, director of the NHS Cancer Screening Programmes, said that the test aims to pick up bowel cancer at an early stage in people with no symptoms, when treatment is more likely to be effective.
"We urge all men and women to accept their bowel screening invitations and advise that you speak to your GP if you are concerned about any symptoms," she added.
Mark Flannagan, chief executive of Beating Bowel Cancer, revealed: "Bowel cancer screening tests are sent free of charge to everyone aged 60-75 in England, but currently only around half are being returned. This partly explains why more than 40 people die from bowel cancer every day.
"We have launched the 1,2,3 campaign to give people the confidence to complete the screening test when it arrives on their doorstep. If everyone took up screening when given the chance, bowel cancer would no longer be the UK's second biggest cancer killer."