if PHE evaluated based on additional peer-reviewed literature, I would expect them to have included those references in their document.
They did 
What might be confusing you is that their starting point was their 2014 report:
PHE commissioned a review of EC in 2014, which covered EC safety [131]. The review found that the hazard associated with use of EC products currently on the market “is likely to be extremely low, and certainly much lower than smoking” and “the health risks of passive exposure to electronic cigarette vapour are likely to be extremely low”.
The report we are discussing is called an 'Evidence Update' and is clearly meant to build on the 2014 report. The executive summary begins: Following two previous reports produced for Public Health England (PHE) on e-cigarettes (EC) in 2014, this report updates and expands on the evidence of the implications of EC for public health.
Clearly you are meant to refer back to that document for further references. PHE next reference the Nutt study and then Hajek's extensive literature review, both of which were published after PHE's 2014 report. Then they look at newer studies to see if they should revise their estimate based on those.
There is an additional Author's Note that accompanies the evidence update which clarifies what PHE have based their figure on and which also references West's evidence briefing to the APPG groups on pharmacy and on smoking and health.
This idea that PHE based their 95% figure on nothing but the Nutt study is getting ridiculous and is highly unfair.
I will accept that the airborne nicotine study is quite weak and PHE could have mentioned that. Nevertheless the levels of cotinine detected were negligible and within the range expected from eating nicotine containing vegetables.
So being exposed to vaping is the equivalent to being exposed to a smoker who is smoking fewer than 7 cigarettes in their presence.
I'm sure you meant in terms of nicotine absorption but it's really important to clarify this. Being exposed to vaping is no other way equivalent to being exposed to a smoker who is smoking even one cigarette in their presence. Of all the potential, theoretical concerns about vaping, nicotine is way down the list.
aside from minor and transient adverse effects at the point of absorption, nicotine is not a significant health hazard. Nicotine does not cause serious adverse health effects such as acute cardiac events, coronary heart disease or cerebrovascular disease,[27, 28] and is not carcinogenic.[29]
We have known for decades that the problem with smoking is not the nicotine, it's the hundreds of other ingredients in tobacco smoke.
In my view, there is little value in studies like this and I don't see much point in building on them save for idle curiosity. Studies measuring cotinine in vapers, and therefore helping to improve efficacy, would be worthwhile though.