Matthew Morley, 37, left the Audi A5 at the scene at junction 11 of the M11 southbound near Cambridge and jumped into another vehicle.
A witness tried to get it to stop but was told Morley’s boss was taking him to Addenbrooke’s Hospital.
On Monday at Peterborough Magistrates’ Court, Morley said he had been “checked out at the doctor’s another day”.
He pleaded guilty to driving without due care and attention and failing to stop after an accident at about 6.30pm on May 29.
Prosecutor Graham Allen said: “He collided with a set of traffic lights, continued across the roundabout and collided with a further set of traffic slights.
“The defendant was seen to alight and walk away from the scene.
“He got into another vehicle before it drove away.”
Mr Allen said a witness claimed the Audi A5 had been exceeding the 40mph speed limit when it mounted the verge and collided with the first set of lights.
He said both sets of lights were “heavily damaged”.
In mitigation, Morley said: “I sneezed and my glasses fell down.
“I’m sorry for what I’ve caused.”
The defendant, of Ramsden Square, Cambridge, was given eight penalty points, fined £466 and ordered to pay £47 victim surcharge and £110 costs.