The statement The evidence of harm from secondhand exposure to vapour is not sufficient to justify the prohibition of e-cigarettes could have been used to describe ordinary cigarettes once upon a time too. They haven't been around long enough for reputable large scale, longitudinal studies to have been carried out.
You missed the start of that quote: International peer-reviewed evidence indicates that the risk to the health of bystanders from exposure to e-cigarette vapour is extremely low. They may not have been around for long enough to do large scale longitudinal studies but in the 10+ years they have been around ecigs have been extensively tested and analysed. The 95% safer figure refers to the risk for vapers themselves who are inhaling vapour frequently and long term.
PHE have stated exactly what this figure is based on (see 'Author's note on evidence ...):
The constituents of cigarette smoke that harm health – including carcinogens – are either absent in e-cigarette vapour or, if present, they are mostly at levels much below 5% of smoking doses (mostly below 1% and far below safety limits for occupational exposure)
The main chemicals present in e-cigarettes only have not been associated with any serious risk
Some flavourings and constituents in e-cigarettes may pose risks over the long term. We consider the 5% residual risk to be a cautious estimate allowing for this uncertainty.
Potential harm to bystanders in light of these facts is immeasurably small because you are just catching an occasional whiff.
E-cigarette use, known as vaping, is not covered by smokefree legislation. E-cigarettes do not burn tobacco and do not create smoke. While debate continues about their absolute level of safety, the consensus across England’s public health community is that e-cigarettes are significantly safer for users than smoked tobacco. An independent review of the latest evidenceii published by Public Health England (PHE) in 2015 found that, based on the international peer-reviewed evidence, vaping is around 95% safer for users than smoking. It also confirmed the findings of PHE’s 2014 independent evidence review,iii that there is no evidence of harm to bystanders from exposure to e-cigarette vapour and the risks to their health are likely to be extremely low. (from Govt. guidance on use of ecigs in public places and workplaces)
I think erring on the side of caution, and not allowing their use in places where smoking is banned, would be the sensible approach to take.
If you are going to use the 'precautionary principle' you need to look at the risks of both action and inaction (permitting and prohibiting ecigs in public places). This is covered in the guide linked above. The risks of prohibiting vaping everywhere smoking is banned include:
Giving the impression that vaping is as harmful as smoking
Making it more difficult for smokers to switch because of the different rate of nicotine absorption when using ecigs (discussed up-thread)
Making it just as convenient to smoke as to vape
Jeopardising vapers' efforts to quit smoking by sending them to stand with smokers
The risks of banning vaping where smoking is banned boil down to making it less likely that smokers will switch to vaping. We know that 50% of long term smokers will die prematurely from their habit, losing on average a decade of life, so these risks are important to consider, hence the PHE guidance.
While some smokers are using them as a way to quit smoking, many are simply using them in order to get around the smoking ban.
It doesn't make any sense to talk of 'getting around the smoking ban' by doing something that isn't smoking 
Almost all vapers are either ex-smokers or current smokers trying to quit or cut down. Frankly I don't care if for some, their initial motivation to try vaping is that they can do it indoors. They might just discover it works, which could lead to a concerted attempt to quit smoking in favour of vaping. This is a good thing and PHE have covered it in their guidance:
to maximise the number of smokers switching to e-cigarettes, vaping should be made a more convenient, as well as safer, option
They are not pleasant to be around and I would prefer not to be exposed to them, regardless of the potential health risks.
Well gosh, if we are going to start banning things just because we personally find them unpleasant and would rather not be exposed to them, I have quite a list 
Shall we start a new thread?
There are also large numbers of children vaping now. The more visible and normalised vaping becomes, the more this is likely to happen. Is this something we really want to encourage?
Children are experimenting with vaping but the number using them regularly without first having been smokers is vanishingly low. This too is covered in the evidence report and in the public places guidance. I'm getting bored of C&P now though, how about you try reading them? ASH do a good factsheet on children and vaping as well.
As time goes on, and the uptake of smoking among children continues to fall rapidly, we might start to see a number of young people who would otherwise have started smoking taking up regular vaping instead. This is a good thing as vaping shows no evidence of being a 'gateway' to smoking and these children won't be facing a 50% chance of early death.
Also, of course, vaping (like smoking) is far more visible to children if everyone is sent outside to do it.