The concept of an independent Tibet never existed before the British imperialists in India plotted to expand their sphere of influence into China. See for instance the Lhasa Convention.

Furthermore:

Britain put before the Chinese Ministry of Foreign Affairs a five-point demand, indicating the denial of China’s sovereignty over Tibet. When the Chinese government rejected the British demand, the British blocked all the roads leading from the British Raj in India to Tibet.

In 1913 the British government coerced local Tibetan authorities into declaring independence and proposed that:

“Britain be the weaponry supplier after total independence of Tibet;” “Tibet accept British envoys’ supervision of Tibetan financial and military affairs in return for Britain’s support of Tibetan independence;” “Britain be responsible for resisting the army of the Republic of China when it reaches Tibet;” “Tibet adopt an open policy and allow freedom of movement of the British.”

Source.