Triumph is the one.
(Sorry NM,

ops: I didn't say that and I should have, you're right. But Triumph is the generally accepted answer to the question "Worlds oldest manufacturer," at least by
What Bike.

).
Founded in 1902, it went into receivership in 1983. The name and manufacturing rights were bought by a man called John Bloor from the Official Receiver. He contracted Les Harris Spares to continue production of the Bonneville for five years until the new factory was ready, which meant production was uninterupted.
The fire in 2002 nearly destroyed the main factory, but they were up and running again the same year, and built another factory in Thailand the following year so they could compete with the Japanese manus.
Soon as my restriction is over, I'm getting a Bonny.
Over to gambogaz1.