Darren Anderton, 49 from Nuneaton, Warwickshire, denies causing the death of 25-year-old Magda Tadaj by careless driving last May.
The Old Bailey heard Ms Tadaj had "catastrophic injuries" when she went under the wheels of his truck.
It happened at a narrow point where the cycle lane ended in St James's Road, Croydon, south London.
Mr Anderton stopped and saw Ms Tadaj lying in the road, waited about eight minutes for paramedics to arrive and then drove off to complete his delivery, jurors were told.
Police officers tracked him down after he completed his delivery and arrested him on suspicion of causing death by careless driving.
The court heard he had left his base in Coventry at about 04:00 BST and driven about 140 miles before the crash.
Prosecutor Ian McLoughlin told jurors Ms Tadaj had just moved in front of the lorry and was about two metres ahead when Mr Anderton began to accelerate, he said.
"Instead of pulling out to allow Ms Tadaj sufficient space or slowing to allow her to continue ahead, the defendant maintained his course and struck her on the near side of his vehicle just in front of the wheel arch in front of his cab," he said.
Mr McLoughlin told jurors there were a number of witnesses to the collision as well as CCTV footage from the lorry.
Jurors were told the defendant had told officers he had been passing when a cyclist had been hit by a car, and that he left the scene as he felt there was "nothing he could do".
On his arrest, he said he had heard a "cry or scream" and looked in his mirror to see a woman lying in the road.
He allegedly said he did not know how she came to be on the ground and did not remember any impact.
The defendant said there were no problems with his mirrors and he was not on his mobile phone at the time.
Mr Anderton said he had been driving for 30 years and had considered himself a "good driver" but now never wants to drive again.
The trial continues.
A lorry driver dragged a cyclist 14 metres under his wheels after he hit her on a narrow road, a court heard.