Lawyers for Dhiren Barot, 34, told he Court of Appeal that he deserved a shorter sentence after pleading guilty to conspiracy to murder.
The Muslim convert pleaded guilty to plotting to bomb the New York Stock Exchange and other U.S. financial targets and to blow up London hotels and train stations with limousines packed with gas tanks, napalm and nails.
In November, judge Neil Butterfield told Barot he would not be eligible for parole for at least 40 years - one of the toughest sentences ever handed down in a British court.
Judges have some leeway in setting minimum terms for life sentences. Barot's lawyer, Ian Macdonald, said that in other circumstances Barot's crime would have attracted a term of 20 or 30 years. But Barot had effectively been ordered to spend the rest of his life in jail, Macdonald told a panel of three appeals judges.
Defending the sentence, government lawyer Edmund Lawson said that even though Barot's plans had not been carried out, it would have been only a matter of time before they created "serious mayhem and injury and death to many thousands of people."
"He was, and he remains, a terrorist," Lawson said.
The judges said they would give their ruling at a later date.