The call comes from Public Health England, as part of an evidence update on the safety of tobacco alternatives which it says should be used more widely as quitting aids.
Meanwhile, Government officials should help manufacturers licence e-cigarettes as medical quitting aids.
Such a move would allow GPs to prescribe the devices to their patients who are trying to stop smoking.
In the independent review, which updates 2015 guidance, experts concluded that vaping only poses a small fraction of the risks of smoking and could be particularly helpful in mental health hospitals.
These patients are often on a long-term stay, and have high levels of smoking and tobacco related harm which could be mitigated by promoting vaping.
E-cigarettes could be contributing to 20,000 new quits each year, they estimated.
But the number of people using the products has “plateaued” and now stands at just under three million people in the UK, according to the review, which was conducted by experts from King’s College London and the UK Centre for Tobacco and Alcohol Studies, the University of Stirling and Cancer Research UK.
One reason behind the stall in uptake could be misconceptions about the levels of harm linked to the devices.
Researchers found that thousands of smokers “incorrectly” believe that vaping is as harmful as smoking and two in five smokers had not even tried an e-cigarette.
In a linked editorial, published in The Lancet, experts from PHE said: “Although not without risk, the overall risk of harm is estimated at less than 5% of that from smoking tobacco; the risk of cancer has been calculated to be less than 1%.”
PHE officials also warned about the risks of tobacco industry efforts to promote “heat not burn” tobacco products as a safer alternatives to regular cigarettes.
It warns that while these combustion-free alternatives currently appear to have some reduced risk, the majority of the research has been conducted the tobacco industry.
Following the review, PHE has made a number of recommendations about e-cigarettes, including a call for the Medicines and Healthcare products Regulatory Agency to support manufacturers to license the products as medical quit aids so they can be made available on the NHS; encouraging any smoker to switch to using e-cigarettes, and calling on NHS trusts to be “truly smoke free”, and as part of this, ensuring e-cigarettes are for sale in hospital shops.
Martin Dockrell, tobacco control lead for PHE, said: “We are saying no smoking anywhere on the grounds [of hospitals], no smoking in the smoking shelter – that shelter becomes a vaping shelter.
“There are two parts to being a smoke-free hospital, one is not allowing smoking on the premises, the other is helping every smoker to quit.
“Some hospitals will decide, especially with their longer-term patients or patients who don’t have a choice whether they are there or not, where it will be appropriate to have spaces indoors to have spaces where vaping is permitted.
“The strongest case for that is psychiatric hospitals because [these patients] have got the highest prevalence of smoking and the highest levels of smoking related harm.
“Single occupancy rooms are quite common in mental health trusts so that makes it very easy for people to vape in a single occupancy room without any annoyance to anybody else.”
On acute hospitals he added: “It is going to be for each hospital to make their own policy but yes, we would certainly encourage them to make at least some single occupancy rooms where people can vape. Of course smoking is prohibited everywhere.”
When asked about indoor communal rooms for vaping, Mr Dockrell said: “There is no reason why a hospital shouldn’t designate some indoor areas where patients and visitors can vape.”