This one could be a little contentious, given all our concerns about increased plod activity to stamp-out this outrageous and irresponsible behaviour.
That said, I achieved 160mph and ran at this speed for about 5 minutes heading south from Le Mans towards Angers in the rain, on the Sat night of the 2001 race.
I also got into a bit of a dice with an Aston Martin Vanquish on the drive back to the Tunnel on the Monday after the same race (the police are pretty much all radar'd-out by Monday). It was on the diversion (dual carriageway) stretch north of Beaumont-sur-Sarthe.
He had me beat, but we ran door handle to door handle at around 160-165mph for a while - and I had the roof down.
It's neither big nor clever, but much safer when the bulk of the race traffic has subsided. My car has a head-up display, which projects the important numbers onto the windscreen, other wise I wouldn't have been able to determine the speed. I kind of get tunnel vision when I'm really stomping on it - not good, but a fact, nonetheless.