Charity Action on Smoking and Health said smoking during pregnancy can cause stillbirths, miscarriages and birth defects.
The latest NHS data shows that 65 out of 365 pregnant women – around 18 per cent – who had their first booking appointment at the trust in February were smokers.
The average number of cigarettes smoked per day by these women was not given for the trust, but the England average for February was seven.
A booking appointment typically takes place between the eight and 12 week point of a woman's pregnancy.
The trust’s rate for pregnant smokers is three times the six per cent target the Government wants trusts to meet by the end of 2022.
It is also well over the England average – 12 per cent of the 48,319 women who had their first screening in February were smokers.
The Barnsley Hospital NHS Foundation Trust had the highest rate of smoking mums for the month, at 27 per cent.
London's Imperial College Healthcare NHS Trust had the lowest, with just one per cent.
Ciaran Osborne, director of policy at Ash, said: “It is vital that all pregnant smokers get specialist support to help them quit successfully.
“But in too many places, this is not happening. The Government must go further, and faster, if it is to achieve its national target to reduce still birth and neonatal death by half by 2025.”
The Department of Health revealed its Tobacco Control Plan in 2017, which included a target to reduce smoking prevalence among pregnant women from 11 per cent to six per cent .
A Department of Health and Social Care spokesperson said: “Smoking rates among pregnant women are at a record low and have been in steady decline since 2010.
“However, this remains a concerning issue, disproportionately affecting women and babies from poorer communities, so we have set an ambition to reduce smoking in pregnancy by a third by 2022.
"As part of our Long Term Plan for the NHS, every smoker admitted to hospital will be offered help to quit – with an emphasis on pregnant women and their partners.”