I think a 1M with tune will do about the same V-max as a 135i with a tune.
I know with my 135i (I have a flash tune
380 PS and 520Nm of Tq and an open V-max) that I have seen 274 kph with my Navi (TomTom), that was in 6th at 6,100 rpms. I also know... quite a few tiimes I have seen 6,300 rpms - but with no Navi. I think that is 177 mph (287 kph) real speed. Not what shows on the speedo! Speedos read higher than true vehicle speed. My car still felt like there was more speed left in her.
Btw... I have PS3's 225's and 255 tires on stock wheels.
Most of the 1erforum.de guys say a tuned 135i should do around 294 kph (actual speed). You only need the right (empty) autobahn and enough of a lead foot to do it. The one series is NOT the best high speed car I have driven. It makes for a bumpy skippy ride at anything over 140 mph.
A stock 1M is limited to 255 kph. Some 1M guys have said they have seen 274 kph... but IF you figgure in that the speedo read 5% high... that is really a 260 kph speed. Ad M has said no higher V-max chip for the 1M like they offer for other M models to go up to a real 280 kph V-Max. I think its because of the jumpy handling of the one series.