That's false, Blackwall tunnel is completely banned for non-motor traffic. The pedestrian path way is for emergency use only and it's blocked off at both ends. Going down there with a bike is suicidal and also prohibited. During my 7 years commute on the A2 I have never seen a single bicycle down the tunnel.

You sure you're not mistaken for Rotherhithe tunnel?

edit: I see you're referring to Greenwich tunnel. Fair points.