Fiona Onasanya, 35, is charged with conspiring with her brother Festus to avoid prosecution after her Nissan Micra was clocked doing 41mph in a 30mph zone.
She told authorities a Russian man was behind the wheel when it was driven through the village of Thorney, near Peterborough on 24 July last year but checks showed he was in Russia with his parents at the time.
Ms Onansanya, who was elected as Peterborough MP in June last year, denies one charge of perverting the course of justice.
Her brother Festus Onasanya, 33, from Cambridge, has admitted three charges of perverting the course of justice, including over the 24 July incident.
The jury at the Old Bailey had been deliberating since Thursday morning and on Friday were told by the judge he would accept a verdict on which 10 jurors were agreed.
After talking for two-and-a-half hours further on Monday, they indicated they could not agree a verdict, even with more time.
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Discharging the 11-strong jury, judge Nicholas 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.”