Fiona Onasanya, 35, allegedly colluded with her brother Festus to escape prosecution for going 41mph in a 30mph zone on July 24 last year.
A Notice of Intended Prosecution (NIP) was sent back to authorities claiming a Russian man was behind the wheel of her Nissan Micra when it was clocked speeding at the village of Thorney, near Peterborough.
However, inquiries revealed he was in Russia with his parents at the time.
Festus Onasanya, 33, from Cambridge, has admitted three charges of perverting the course of justice, including over the July 24 incident.
His sister, who was elected as Peterborough MP in June last year, denies one charge of perverting the course of justice.
Judge Nicholas Hilliard QC sent the 11-strong Old Bailey jury out to deliberate on its verdict just after 10.30am last Thursday.
On Friday afternoon, he said he would accept a verdict on which 10 jurors were agreed.
After two-and-a-half hours of deliberations on Monday, the jury indicated they could not agree a verdict, even if they had more time.
Discharging the jury, Mr Hilliard QC said: "I have had a note from you saying you do not need any more time.
"Thank you very much for the evident care and attention you have given this case. The case will have to be retried in due course in front of a different jury."
Speaking to Premier shortly after her election victory she explained her role as a Christian in parliament.
She said: "Scripture says to go into all the world – the world isn't just a geographic world – its spheres of influence.
"So I'm going into the world of politics."
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