Michael Baigent and Richard Leigh claim U.S. author Dan Brown stole the idea that Jesus had a child from their 1982 book "The Holy Blood and the Holy Grail."
Baigent and Leigh wrote their book with a third author, Henry Lincoln, who is not taking part in the suit due to illness, the BBC said.
Justice Peter Smith is expected to take time to read the material involved before witnesses, including Brown, give evidence, the Financial Times said.
Included in Brown's novel is a character called Leigh Teabing, whose name is an anagram of Baigent and Leigh.
Brown's book has sold more than 40 million copies worldwide, and has been made into a $100 million film, due to premiere this year at the Cannes film festival.
If Random House loses, lawyers say some form of royalty sharing deal would probably be arranged between the parties.