These are entirely paper-based prosecutions in which someone is accused by post of a minor offence, such as a car-insurance violation, and has to defend themselves by letter.
But 550,000 of those accused never even replied, Alexander said, raising questions about how many understand the consequences.
“They don't enter a plea one way or another,” she said.
“It just heads straight off to the magistrates' court.
"And so I think, in the round, we need to improve the way in which the single justice procedure is operating.”
Questions around the SJP’s safeguards grew this year, after a landmark court ruling found up to 74,000 fines should be quashed because railway companies had been wrongly using the procedure to prosecute people accused of fare dodging.
The government would not scrap the SJP, Alexander said, but there was a case for stronger safeguards, including ensuring all cases were justified.