Britain came into contact with Tibet in the late nineteen century through its occupation of Burma. Upon 1st contact, the Tibetans historical reaction was to deny entry to the British. They had no wish to trade with Britain. So the Tibetans deferred Britain to China for negotiations. China, however, had already given British permission to trade in Tibet.

When Tibet continued to deny the British entry, Britain sent 2 military expeditions into Tibet, causing the 13th Dalai Lama to escape from Lhasa with his entourage. After a brief exile, the 13th Dalai Lama agreed to a truce by allowing British to enter Tibet and also agreed to "war reparations" to Britain.

China became increasingly worried that Britain had managed to gain a foothold in Tibet, and that Britain may annex Tibet. China demanded and received British treaty recognition that "Tibet is a part of China".

Tibet, realizing China's declining power under the onslaught of foreign powers, attempted to persuade Britain to give Tibet military aid, to reclaim "Historical Tibet", areas of Tibetan Empire once held in the 8th century.

Britain, however, was concerned about increased Russian influence in China, and feared that if Britain provided Tibet military aid, it would alienated China and drive China to a Russian alliance. Britain thus refused to give Tibet military aid, and refused to help Tibet assert independence.

In a Tri-parte Treaty between Britain, Russia, and China, China was formally recognized to have "Tibet as part of China", and Britain and Russia both agreed NOT to negotiate directly with Tibet, except through China or her consent.

Britain's primary interest in Tibet was not so much trade, but rather creating a buffer zone for British Burma.

As far as CIA, the story is equally geopolitical.

US had little interest in Tibet during WWII. However, in the 1910's through the 1930's, Tibet began to solicit and receive military aid in weapons and training from Imperial Japan.

The current Tibetan "National Flag" of the Tibetan Exile Government is actually a Japanese design, incorporating the traditional Tibetan code of arm on the fore ground, and a rising sun with radiating rays in the background (One that's very similar to the Imperial Japanese military Rising Sun flag).

Japanese weapons were sent to Tibet, and Japanese military training manuals were printed in Tibetan.

Japan, at the time, was a militaristic Empire, with a state sponsored fundamentalist Zen Buddhism Church that indoctrinated its people to combine Nationalism and Religious zeal.

This form of Buddhism as the backbone of a military society, appealed to the Buddhist Theocracy in Tibet. Tibet began to consider Imperial Japan as its "Buddhist Patron".

This partially explained Tibet's refusal to join the League of Nations, which could have helped Tibet in its "independence" drive. But with Tibet finding Imperial Japan as its "patron", Tibet was less concerned about "independence", and becoming more attracted to the Japanese "Greater Asian Co-prosperity Sphere" idea. Japan had already attempted to extend this "sphere" to Mongolia during the same time. Consequently, Tibet declared neutrality during WWII. And Tibet briefly fought China to regain its "historical territory" during WWII.

Perhaps partially due to Tibet's tie to Imperial Japan and Nazi Germany during WWII, the Ally Powers continued to recognize Tibet as part of China, which was 1 of the 5 Major World Powers during WWII. It was again, geopolitical in nature.

After WWII, Republic of China (ROC) held the legal title to Tibet as part of China. And the other nations did not question it. Tibet also did not seem to question it much. ROC troops had not made any advances to Tibet. Tibet assumed that it would continue the historical relationship with China along the "Patron-Priest" relationship. However, Tibet's assertion of "historical territory" was becoming a problem for ROC government, but ROC government was busy engaged with the Communist forces during the Civil War.

Once the Communist government of PRC won the Civil War, they turned their attention to Tibet. They were able to use their forces to press the Dalai Lama to sign the 17 point agreement, though Tibetan Exile Government claimed that this agreement was "under duress" and thus null and void. (However, this agreement is merely the agreement for setting up the Chinese administration of Tibet as a province. It was not intended as a "Treaty".)

Small number of Tibetans did not go along with the new Chinese arrangement and went into Exile in Nepal.

CIA, after the Korean War, decided to recruit these exiles by the hundreds, trained them in Colorado, and then air dropped them back into Tibet to conduct ambushes and raids on Chinese military in Tibet. CIA support for Tibetan rebels began in 1956. Rebels set up a base in Mustang, Nepal.

The goal from the CIA was never about "Tibetan Independence", but rather to harass China and force China to waste large amount of resources dealing with this problem in Tibet.

But soon, in the late 1960's, US sought China's help to aid the Afghan resistance war against USSR. China required US to shut down all its support for the Tibetans. And the CIA abruptly cut off Tibetan Rebel's funding. Under pressure from US and China, Nepalis government threatened to bomb Mustang Rebel base. The Dalai Lama ordered the Rebels to pull out of Mustang.