Rotherhithe tunnel?

I've done it a couple times.
It's quite an experience and you can pick up some serious speed when there isn't too much traffic. The sidewalk is VERY narrow and has blind bends which slow you down, you want to get through there quick as breathing becomes an issue with the fumes down there. Unless the traffic is very busy/slow I'd recommend you stay on the road as you'll be faster.

Go for it!

I did't even consider the pavement but +1