If you drove round the M25 clockwise in the slow lane, how much further would you drive than if you went anti-clockwise in the slow lane?

Surely the same distance, assuming you went at the same speed both times? And allowing for traffic congestion...
I don't believe it should make any difference what direction you move, if you're going the same distance?
Troll

Ah, but... Clockwise will be further, because the slow lane is on the very outside of six (or eight?) lanes (three or four in each direction), while the anticlockwise slow lane is on the very inside. Think of it for a moment as two concentric circles. In real life, it wanders about a bit, bit it must be further. Not a lot, but measureable. (Think of the staggered start positions on a running track - if they all started in line the poor beggar on the outside would be running further.)

Pi (3.1415926535) x Diameter.

Are we speaking about the outer wheel distance or the inner wheel distance? Remember the Speedo/Odo is directly attached to a gear that is turned by the output shaft of the transmission. The outer wheel is traveling a greater distance.

How wide a car are we speaking of? This certainly changes the diameter of the circle.

Is the road dry? A wet road would allow for a minute amount of lateral slippage reducing/increasing the overall distance by a few millimeters.

Just picking nits to come to a more finite answer.

Well I have an answer based on concentric circles; doesn't look right but with the absence of any other figure I will go for it: 380 metres.
There - I've said it!

You also have to allow for the fact that the M25 is not continuous as it becomes the A282 at the Dartford Tunnel & Queen Elizabeth II bridge

Well, just to get a ball-park figure (totally inappropriate for a British question I know). Assuming the average distance between the slow lanes is about 100 feet, and the route is circular, then the difference would be about 2pi times 100, or about 600 feet, or about 200 metres.