According to the Mail on Sunday, the couple approached Staffordshire County Council two years ago after several failed IVF attempts costing over £20,000.
A social worker visited them and the couple – referred to as 'Abigail' and 'Brian' – went through a variety of medicals and interviews.
After proving they were 'of sound character and financially capable of raising a child', the couple thought they were on track to adopt.
But when a social worker saw Brian using an e-cigarette, everything changed.
At the beginning of the process, Brian, 45, was a light smoker, but towards the end - he told the paper -: "I'd stopped smoking completely and hadn't had a real cigarette in months. I was using e-cigarettes as a cessation aid, to ease the nicotine cravings."
The social worker warned them the council did not allow smokers to adopt young children, although she was unclear about its position with e-cigarette users.
The next day, she revealed that the council would not place a child with anyone who had used e-cigarettes in the previous 12 months either – despite there being no evidence that 'vaping' is harmful.
In October, she confirmed in an email: "Should you both become non smokers/e-smokers over a 12-month period, then you could of course reapply."
Abigail, 43, told the paper: "It made us feel judged and worthless, that you are a lesser person if you smoke e-cigarettes. They seem to be seeking adopters who are perfect. But we are like lots of ordinary families."
She said she believed she and her husband had fallen victim to 'over-zealous, politically correct' social workers.
Many councils cite guidance from the British Association for Adoption and Fostering (BAAF), which recommends 'users of e-cigarettes be considered smokers' until concerns about the devices are cleared up.
However, other councils cite alternative guidance from the Fostering Network, which says that people 'should not be prevented from fostering or applying because of e-cigarettes use'.
Professor Robert West, director of tobacco studies at University College London, said the policy was 'badly thought out' and would cause 'significant harm'.
He said: "There are so many misconceptions about e-cigarettes that policy makers and the public are getting very confused."
Staffordshire County Council now says it doesn't have a policy of refusing to place children with e-cigarette users who did not smoke tobacco.
Councillor Mike Lawrence said: "Applications from people who use e-cigarettes are considered as long as they have not smoked tobacco for over a year."
He also apologised to the couple, saying that 'they were given the wrong information' and pledged to make the situation clearer to other applicants.
According to the paper, at least 13 other councils across England state they will not place under-fives with e-cigarette users. They include Bury, Kirklees, North Tyneside, Durham, Warrington, West Sussex, Poole, Cornwall, Camden, Wolverhampton, Sandwell, Walsall and Dudley councils.
Many cite the BAAF, which is concerned that e-cigarettes 'may act as a "gateway" for children and young people to start smoking'.