The hook-handed, one-eyed former imam of the Finsbury Park mosque in north London was jailed for seven years in February.
During his trial at London's Old Bailey, the prosecution claimed he was a recruiting sergeant for global terrorism, preached "terrorism, homicidal violence and hatred" and incited his followers to murder non-Muslims and Jews.
He was also convicted of possessing a terror manual, which featured a dedication to Al Qaeda leader Osama bin Laden and a list of potential targets including Big Ben in London and Paris's Eiffel Tower.
Hamza, 48, who was found guilty of 11 out of 15 charges, is wanted in the United States, which has requested his extradition.
Edward Fitzgerald, Hamza's lawyer, told the court that it was impossible for the cleric to have received a fair hearing due to the delay in putting him on trial.
The sermons in question took place up to 2000 and since then, the September 2001 attacks on the United States and the July 2005 London bombings took place and Hamza had been subjected to a campaign against him by politicians and the media, Fitzgerald said.
"It was unfair to put the appellant on trial in 2006 for speeches made in the years 1997 to 2000, in respect of which the police had taken no action at the time," he told the three appeal court judges, including the lord chief justice of England and Wales.
"Because of this delay, a series of subsequent events and a campaign conducted by the media and leading politicians against him came to prejudice his chances of a fair trial.
"It was therefore impossible for him to receive a fair trial in 2006."
Hamza is being held in the high-security Belmarsh prison in south-east London and was not present in court.
"It can be regarded as oppressive and unfair for a trial to go ahead when the prosecution will benefit and the defendant suffer from the additional prejudice caused by the state's own delay," Fitzgerald said.
He also argued that there was no case to answer on the incitement to murder charges.
"The solicitation in this country of non-citizens to acts alleged to involve the murder of foreigners abroad is not an offence contrary to Section Four of the Offences Against the Person Act 1861," he said.
Fitzgerald also raised the highly-publicised decisions of Britain's then interior minister, David Blunkett, to strip him of his British citizenship and of the United States authorities to seek his extradition.
Hamza was born in Egypt but acquired a British passport through marriage.
The two-day hearing is expected to conclude on Tuesday.

Copyright AFP (Agence France-Presse), 2006