They have published the results of a trial involving 600 women from Glasgow in the British Medical Journal.
More than 20% of the women offered vouchers stopped smoking, compared with 9% given normal NHS support alone. The Royal College of Midwives said incentivising healthy behaviours using money was "not ideal" - and expensive.
Women taking part in the trial had breath tests - as well as providing saliva and urine samples - to check whether they were smoking. Blood samples were monitored too.
In the randomised controlled trial, the researchers assigned the women into two groups of around 300. All were from the area covered by NHS Greater Glasgow and Clyde, which has large pockets of deprivation. This evidence shows that the money is the hand they need to pull them out of their addiction ”
The control group were offered a face-to-face appointment with a smoking cessation adviser, as well as four follow-up phone calls and free nicotine replacement therapy for 10 weeks. The financial incentive group received that standard support - as well as £50 in their first appointment, £50 if a breath test later suggested they had stopped smoking, and then a further £100 after another 12 weeks.
The final £200 voucher was given if another breath test at 34-38 weeks in pregnancy confirmed there was no carbon monoxide exhaled. After a year, 15% of women who received the vouchers had managed to stay off cigarettes, compared with 4% in the control group. The women used the vouchers at High Street stores such as Iceland, Argos and Mothercare.
The researchers from Glasgow and Stirling universities say providing the vouchers is cost-effective for the NHS, because smoking in pregnancy raises the risk of miscarriage and stillbirth.
But schemes using financial incentives to promote healthy behaviour have been criticised as "bribery" - and this remains a controversial area of research. The authors say in the BMJ: "This study provides substantial evidence of a promising and potentially cost-effective new intervention to add to health service support.
"Smoking during pregnancy remains a major health problem, resulting in the deaths of an estimated 5,000 foetuses and babies each year in the UK." "It is responsible for tens of millions of pounds in extra healthcare spending." "Receipt of financial incentives can contribute to needed household income in advance of the arrival of a baby in low-income households."
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