Many years ago I tried something similar starting from Baker street tube station. I had borrowed a map from my Aunt.
I had thought I'd find NCR 1, and it would all be good. Well the signs were hard to follow and I got lost, so I then saw a sign for Dover, so figured I'd follow that, it would at least get me out of town. The road started as one lane each way, then two lanes each way, then three lanes each way, and then three lanes each way with blue flashing lights.
I explained to the nice police officer what I was trying to do, and that I was lost. I took out the map and we tried to find a batter route. The map was weird. It didn't have an M20... or an M2... or the M25... and was printed in 1975...
And that's how I got a police escort from the M20...
I eventually just followed the A2. Which was not ideal, but by the time I had got out of the M25, it was gone 10pm anyway...
J