There is A LOT of interesting history behinds the choice of Bond's gun...
When Fleming wrote Casino Royale, Bond's debut novel, he wrote him as being issued a Beretta 418, as this was a weapon Fleming himself used whilst attached to British intelligence in the war years. This gun features a cameo in Skyfall:
However, after the novel's debut and wide success, he was wrote by a former soldier and distinguished gun expert Geoffrey Boothroyd, who took issue with the firearm provided, which was known for it's 'lack of stopping power', I.E it's low calibre for a field primary sidearm.
Being an expert of some renown, Fleming took heed of Boothroyd's suggestion; he even honored him in the film as the character 'Major Boothroyd', which is the reason people often erroneously believe Geoffrey Boothroyd was in fact a high ranking Major; he was, in real life, no such rank.
Their discussions culminated the Boothroyd's suggestion of a Walther PPK 7.65mm, as an automatic weapon with considerable caliber that, importantly, lent itself to concealment and quick draw; essential tools for an operative.
Interestingly, before the look of Bond's gun became Iconic, he was written as having a number of firearms to be utilized for differing purposes. One of these was a custom Snub-nosed Chopping .357 Magnum revolver, with a third cut off the trigger and the subsequent guard removed entirely.
Before the Walther, this was the weapon most closely associated with Bond, and interestingly, has a history of its own: during a triple murder investigation (which resulted in the eventual arrest of Peter Manuel, the 'Beast of Birkenshaw'; the psychopath on which Brian Cox based his portrayal of Hannibal Lecter for Manhunter), the same unique gun was used. So rare was this custom weapon, that Boothroyd himself was questioned in connection with the murders; and was only exonerated when he was able to prove by telegram/parcel receipt that he had sent his weapon down to Fleming's illustrator to be drawn for the cover of From Russia with Love.
After the excitement regarding the confusion, it seems Fleming tried to distance bond from the gun, now famous for all the wrong reasons. Additionally, at the end of said novel (From Russia with Love), Bond's Beretta get's stuck in his holster (due to the exposed hammer), which nearly gets him killed.
By the next novel, Dr. No, Bond is told, no doubt due to word of his costly issue with the Beretta getting back to his quartermaster in part of the subsequent debriefing, to permanently adopt a more appropriate weapon; the PPK.
The reasons as to why Bond is described (perhaps falsely) as the 'only' operative that carries the PPK are in light of a few contributing factors;
Bond is explicitly ordered to use this firearms as a result of his previous near fatal mishandling of the Beretta.
Field Operatives have preferences, and familiarity with certain weapons which the would favor. The introduction of a new standard does not necessarily command its immediate adoption.
Firearm improvements are introduced constantly, but an operative will always favour the weapon with which he has most experience. It's possible that the standard changed again quickly afterwards, and Bond was the only agent caught within it's remit; or that all other agents have been killed in the interim!
By any means, such was the interest in Bonds arsenal that Connery himself fronted a 'behind the scenes' documentary, discussing Bond's weaponry choices and reasoning...
