You cannot arrange it yourself, and you cannot go independently
The UK foreign-ministry advice states, verbatim: you must get a permit to travel to Tibet and the Tibet Autonomous Region (TAR) through a specialist travel agent in China, and you must also travel on an organised tour. So the two things a visitor most wants to do — apply directly, and travel independently — are both ruled out: the permit runs through an agent, and the trip is a tour.
UK foreign-ministry advisory: UK Foreign, Commonwealth and Development Office (gov.uk) — Foreign travel advice: China — Regional risks (source standing advisory page; read August 9, 2026)