Stumbled upon this late last night because I had been contemplating walking to work instead of the Metro.
These tunnels are closing sometime in the near future for 12 months to allow refurbishment and the public will be given one month notice. There will be a free shuttle bus service operating up to every 20 minutes. I immediately assumed that the cycle-friendly Lime buses by Go North East would be used, but apparently a cycle trailer towed by the shuttle bus will accommodate 16 bikes at a time instead.
I'm not sure if normal public service vehicles can carry trailers? I would imagine it would be a small minibus that runs the service to save on costs.
Full details can be found here -
http://www.tynepedestrianandcyclisttunnels.co.uk/faqs/
NEB Admin Team
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Tyne Pedestrian and Cycle Tunnels Closure