Criminal trespass charges against the pair, from Hereford, were dropped for "evidential reasons".
However, the schoolgirl claimed the case was dropped to avoid damaging commercial ties with Japan.
Sophie said: "If they have resources to spend on trivial prosecutions like this, they should really be putting them into the fight against Japan's barbaric whaling industry, which is illegal under international law."
A spokesman for the CPS said it had dropped the charges for "evidential reasons".
He said: "After further review it was decided there was no longer a realistic prospect of conviction."
But Mr Wyness, a shop worker, said he and his daughter were guilty and had gone to court expecting to be sentenced.
"This is clearly a travesty and is bringing British law into disrepute.
"They're saying lack of evidence and yet we were guilty. They have all the evidence they want for a conviction."
District Judge Quentin Purdy lifted an order at the City of Westminster Magistrates Court banning the publication of Sophie's name, after legal representation from the BBC.
After the court hearing Sophie and her father delivered a letter to the Japanese embassy asking the ambassador to put pressure on his government to end whaling.
Security staff at the embassy stopped the pair entering the building, but agreed to pass the letter on.