The authors of the review said pregnant women who smoke should be encouraged to switch to e-cigarettes, though they said research on this is only just underway.
Joyce Robins, of campaign group Patient Concern, told The Times that it was a bad idea to use up much-needed spaces in hospitals to create vaping areas.
"We really want to get the message out that smokers really should consider using an e-cigarette because they're a lot better for them", adds Newton.
It also suggests at least 20,000 people a year are quitting smoking with the help of vapes.
Experts from King's College London, the UK Centre for Tobacco and Alcohol Studies, the University of Stirling and Cancer Research UK concluded that vaping only poses a fraction of the risk of smoking.
"It would be tragic if thousands of smokers who could quit with the help of an e-cigarette are being put off due to false fears about their safety".
"When people smoke tobacco cigarettes, they inhale a lethal mix of 7,000 constituents, 70 of which are known to cause cancer", she says.
Ancient arachnid: 100-million-year-old spider found trapped in amber
However, they are also equipped with tails which are also common in even older spider relatives called uraraneids . The new animal resembles a spider with its fangs, four walking legs and silk-producing spinnerets at the rear.
But Professor Martin McKee, of the London School of Hygiene and Tropical Medicine, pointed out that a more extensive review in the USA, published two weeks ago, was much more "cautious" about e-cigarettes' long-term safety.
Doctors and nurses can not prescribe e-cigarettes to smokers wanting to quit because none has yet been licensed by the Medicines and Health Care Products Regulatory Authority (MHRA).
The body also wants hospitals to become completely smoke-free.
"There are two parts to being a smoke-free hospital", he said.
Martin Dockerell, PHE tobacco control lead has advised that smoking should be completed banned from hospital grounds - with smoking shelters re-purposed as vaping shelters.
Mr Dockrell said there was no reason why "a hospital shouldn't designate some indoor areas where patients and visitors can vape". But PHE believes many aren't bothering to try e-cigarettes in the mistaken belief that they are just as harmful.
"Our new review reinforces the finding that vaping is a fraction of the risk of smoking, at least 95 percent less harmful, and of negligible risk to bystanders", said John Newton, a professor and director for health improvement at PHE. Thousands of smokers think e-cigarettes are just as risky and 40% of smokers have not tried one, it says.