TLDR; Under several imperfect assumptions, there will be approximately 1.4 million voters (2.9% of the total) who can vote in the 2017 election, but couldn't vote in the 2015 election. Details below.
As noted in comments, the latest British Census is from 2011. Very roughly speaking (we'll clean it up later), people who were 12-13 in 2011 would've been 16-17 in 2015 (ineligible to vote) but 18-19 in 2017 (eligible to vote).
According to the Census (1, 2) we have:
- 12 year old males: 377620
- 13 year old males: 383672
- 12 year old females: 359875
- 13 year old females: 365950
for a total of 1,487,117 people.
However, even if this data were taken on May 7th, it would only include people turning 18 between May 7th 2015 and May 7th 2017. To adjust for the extra month, we multiply by 25/24 to get 1,549,080. Of course, that's just an approximation.
We can also say that, roughly speaking, about 2000 people turn 18 everyday in the United Kingdom.
According to Electoral Commission's provisional figured published ahead of the EU referendum there were 46,354,197 people "eligible and registered" to vote in the May 2015 referendum. However, this doesn't include people who were eligible but not registered.
Going back to the 2011 Census, we see there are 52,063,665 people who were 14 or older in 2011, and thus, roughly speaking, eligible to vote in May 2015.
Dividing 46,354,197/52,063,665 we see that, again roughly speaking, about 89% of people 18 or older were registered to vote in the May 2015 referendum.
If you accept the 89% rate applies to young voters, that gives us 1,379,202 new voters between the two elections, meaning new voters will make up about 2.9% of the vote, enough to swing a close election.
Disclaimers and minutiae:
Although I use precise numbers above, these are only estimates. For example, you should read "52,063,665" as "about 52 million".
I assume the voting age in Britain is consistently 18 and that age is the primary factor in determining whether otherwise eligible people can vote; if this is untrue, my numbers will be off by a bit.
Since I provide sources, you should check my work if you plan to use it for anything important.
Some people eligible to vote in the 2015 election have or will die before the 2017 election. You could probably find statistics to include them in the estimated voter count, but I didn't. Generally, the death rate is fairly small, since it roughly reflects the number of people born 70-80 years ago.
As noted in the comments, the UK's population includes people who are ineligible to vote. Additionally, the UK's electorate as defined above, excludes people who are eligible to vote but haven't registered to do so. There is some discussion on eligible-but-unregistered voters at:
I assume that women can vote in the UK, and that British age at the same rate as normal people.
Even though I use the phrase "British" above, I'm referring to the entire United Kingdom excluding Gibraltar, but including Northern Ireland.