Mums in Derbyshire, central England, and its neighbour South Yorkshire, will be offered shopping vouchers worth Ģ120 ($200, 140 euros) if they breastfeed for the first six weeks, rising to Ģ200 if they continue for six months.
Some 130 women from deprived areas will take part in the pilot scheme, which aims to establish whether financial incentives can boost a practice believed to bring significant health benefits to newborn babies.
"The UK has one of the worst breastfeeding rates in the world and breastfeeding rates vary very widely across different parts of the country," said Clare Relton of Sheffield University, which is running the pilot in collaboration with the government.
"Babies who are breastfed have fewer health problems such as upset tummies and chest infections, and are less likely to develop diabetes and obesity when they are older."
A six-week-old baby born into an affluent family in Britain is four times more likely to be breastfed than one in a deprived area, she added.
Britain's National Health Service recommends that mothers feed their babies only breast milk for the first six months -- but this only happens in 34 percent of cases, according to Relton.
Breastfeeding is "stigmatised" in parts of Britain, she added -- including through advertising for formula milk that can make it seem a less attractive option.
But Janet Fyle, policy advisor to the Royal College of Midwives, said the reluctance to breastfeed amongst some mothers was a deeper cultural problem that would not easily be solved by handing out shopping vouchers.
"In many areas, including those in this study, there are generations of women who may not have seen anyone breastfeeding their baby, meaning it is not the cultural norm in many communities," she said.
Many women also struggle to get the baby to feed properly, while others find it difficult if they go back to work soon after the birth.
"The motive for breastfeeding cannot be rooted by offering financial reward. It has to be something that a mother wants to do in the interest of the health and well-being of her child," Fyle said.
The scheme could be rolled out nationally next year if it successfully boosts breastfeeding rates, organisers said.
The initiative will not be rigorously policed, simply relying on the mothers' midwives to confirm that they are breastfeeding.
Women taking part in the pilot scheme will be able to cash in their vouchers at supermarkets and high street stores.