The two historians who lost their plagiarism case against the British publishers of the best seller “The Da Vinci Code” by Dan Brown turned to the Court of Appeal in Britain yesterday in an effort to reverse their loss in a case that also saddles them with a legal bill of more than $2 million, The Associated Press reported. Lawyers for the historians, Michael Baigent and Richard Leigh, argued that the “vast amount of skill and labor” they expended in writing their book “The Holy Blood and the Holy Grail,” first published in 1982, is “protectable.” They contend that Mr. Brown stole significant parts of it for his novel. Both books are based on the theory that Jesus and Mary Magdalene married and had a child, and that the bloodline continues to this day. In April, Justice Peter Smith ruled that Random House had not breached the copyright of “The Holy Blood and the Holy Grail,” and Mr. Baigent and Mr. Leigh were ordered to pay 85 percent of Random House’s legal bill, estimated at $2.6 million. In a statement, Random House expressed regret “that more time and money is being spent trying to establish a case that was so comprehensively defeated in the High Court.”