Horne, who undertook a 68-day hunger strike last year in a protest designed to bring an end to vivisection, is serving what is believed to be the longest sentence given for animal rights offences.
The former dustman was convicted at Bristol Crown Court in December 1997 of charges of arson and attempted arson after causing millions of pounds in damage to shops on the Isle of Wight in 1994.
Yesterday, Lord Justice Tuckey, Mrs Justice Smith and Mr Justice Gray, sitting in the Court of Appeal in London, rejected his claim that his conviction was "unsafe" and that his sentence was too long.
Horne, 46, from Northampton, was present in the dock yesterday, flanked by four security officers, to hear the court rule against him.
The court was packed with his supporters, who earlier handed out leaflets declaring Horne's "innocence" in the Isle of Wight arson attacks.
After Lord Justice Tuckey gave the ruling of the court, some people in the public gallery stamped their feet and there were shouts of "It's disgusting", and "Shame on British justice".
Horne had claimed in his appeal that the judge at his trial, Judge Simon Darwall-Smith, had given a misdirection to the jury during his summing- up, thus rendering the conviction "unsafe". Lord Justice Tuckey said that although the judge had made an "error" during his summing-up, it did not render the conviction unsafe.
He said with hindsight, the judge should have said nothing about possible alternative "candidates" for the Isle of Wight fire bomb attacks, but this should be seen in the context of the standard of proof required.
He added: "This court has to ask itself if it [the judge's direction] renders the verdict unsafe - we do not think so.
"We can see no reason for thinking that the sentence in this case was obviously too long. It seems to us that although it was a long sentence, it was a sentence which was the appropriate sentence for these very serious offences."
The Crown contested Horne's appeal, submitting that the evidence against him was "overwhelming".
Sentencing Horne in 1997, the trial judge told him: "This was urban terrorism for a particular cause and objective. You put communities in terror. But I do accept that you did not intend an attack on human life."
During his trial, he denied the Isle of Wight offences, but admitted to attempted arson charges related to placing timed incendiary devices in two stores in Bristol in July 1996.
Horne went on a hunger strike in an attempt to force the Government to set up a royal commission into vivisection.Reuse content