The Fraser Hart I dealt with were excellent.
They were clear that it was a central buy (60 in the first batch) nationally that their buyer had secured from Tudor, and all the ADs were in a strict queue to acquire them from HQ.
BTW the blue NATO is from the BB Blue, I have had one for ages (bought here), and I wear it on my Pelagos quite regularly. It was not supplied with the watch (which I got on bracelet).
As stated before, the Black (with red stripe) NATO that Tudor also offer for the BBGMT can be bought separately from an AD for £150. There is a month waiting list for the strap, apparently
Note also that the Crafter Blue Rubber (see above) which is sold as a BB strap only, does not fit the Pelagos at all, which is a shame. But the lug holes on the Pelago are a lot closer to the case than on the BB.

Dave