Before this announcement and after walking free from court, Griffin told waiting reporters: "If the Crown Prosecution Service feel they must continue to persecute us for speaking the truth, we will see them in court."
He added: "If they want to do it all over again, well we're here."
Griffin faced a total of four charges relating to two speeches and Collett faced eight charges relating to four speeches.
The jury found Collett not guilty of four race hate charges and Griffin was cleared of two race hate charges.
The jury was later discharged after failing to reach verdicts on the remaining charges.