The 35-year-old solicitor was expelled from the Labour Party after being found guilty in December last year.
She was jailed for three months at the Old Bailey in January and was released from prison after serving one month behind bars.
Representing herself at the Court of Appeal on Tuesday, Onasanya told the court: "The charge against me was perverting the course of justice.
"I said from the outset, and I still maintain my innocence, that I did not do that."
But she was refused permission for a full appeal by three leading judges.
Jurors at the Old Bailey were told that she colluded with her brother Festus after her car was clocked speeding at 41mph in a 30mph zone in the village of Thorney, near Peterborough, in July 2017.
She was sent a notice of intended prosecution to fill out, but it was sent back naming the guilty driver as Aleks Antipow, an acquaintance of her brother, who was away visiting his parents in Russia.
Festus Onasanya, 34, from Cambridge, was jailed for 10 months after he admitted three counts of perverting the course of justice over speeding, including the July 24 incident.
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