A 276AW/1BB is off a BSA B31 1946 to 1948 and may have the bowl on a 3 degree or 7 degree angle or has it got the proper M20 bowl of 1B which is no angle. If you have a 7 degree angle bowl you may find it will play up on bendy roads as too rich on some bends and too lean on other bends but should not upset the starting. If the bike is starting and then stopping real quick has it got stale fuel?
This might sound a bit daft but it's happened to mne when restoring older bikes.
A rat or mouse family makes a home in the silencer and they bring in enough bedding material to block the pipe. Successive generations bring in more material. The bike will start eventually but will not rev above idle. Worth checking...