The only small possibility that might help you is if you could claim that the other driver was putting you at serious risk, eg: trying to ram you off the road, which has been used by a few celebs.
However, that might work at 100mph (maybe), but doubtful it would work at 116. To be honest, unless you're driving some super-powered car, hitting 116 would take time and thus would probably reduce the chances of this working. Also if not mentioned to the officers at the scene to investigate, it's unlikely to work either.
Best answer is not take a solicitor and be humble at court, oh and if you own a flash car, sell it and go buy a Golf. I know someone who was done at 124 (!) and got a 6 month ban for this, although he didn't have any points. Oh....you'll need the pilots licence to pay for your next car insurance bill.