Could you tell me where I might apply for my grandfather's British War Medal his name is John Percy Blackburn, he joined the NREF in Murmansk 1918 Middlesex Regiment and was a 2nd lieutenant?
As Antony states, WW1 Campaign Medals can no longer be issued on behalf of those who never received them. According to the MoD site describing eligibility for WW1 Medals
All World War 1 medals were issued to the recipient or next of kin after the war ended. You can only apply if the medal was returned, and you can provide a medal card or roll which includes this information.
If the veteran has died, you must be the official next of kin. The general rules are:
the person’s spouse or civil partner has first claim to the medal, and then the eldest child
if there’s no spouse or child, the eldest grandchild is entitled to apply
In general terms, it might have been that he never applied for them in the first place. Officers in WW1 had to apply for their campaign medals - unlike enlisted men, who got their's sent automatically. You need to check the Medal Index Cards (Ancestry or TNA) to see if he applied or not. For instance, if I recall correctly, JRR Tolkien, a lieutenant in WW1 who saw action, must not have applied as he isn't in the Medal Index Cards.
The other thing to bear in mind is that eligibility for the Russian campaigns is complex and he might not have been entitled. I'm still not totally sure, for instance, why my G-uncle, in the Caucasus post 1918, wasn't entitled.
In this instance (thanks to @AndyW for the prompt) we can see from the Medal Index Card that
2/Lt JP Blackburn applies for BW Medal 14-9-19
At this point he was at 9 Cann St, C-on-M, Mancester. However, the medal appears to have been returned 1-8-20 (or that might be the date of the annotation). Why it was returned, I don't know.
Are you sure he was never issued with it? Check the medal cards on Ancestry to check.
I applied for my Father in Law's military record from WW2 and when the papers came back they said he had never applied for his medals and included a form for my wife to sign if she wished to claim them. They arrived in the post a couple of weeks later.
You can probably do the same thing for WW1 but bear in mind that not all WW1 military records survived, again those that did are on Ancestry.
According to the MoD website, you can only apply for WW1 medals if the original was returned: https://www.gov.uk/apply-medal-or-veterans-badge/apply-for-a-medal