Radical Muslim cleric Abu Hamza al-Masri is appearing before magistrates by video link.
Mr Abu Hamza was arrested in May and is being held at Belmarsh high security prison while he fights extradition to the US on charges related to terrorism.
The London-based cleric is accused of trying to set up a terrorist training camp and being involved in a kidnapping in which three Britons were killed.
On her way to court his lawyer said Mr Abu Hamza’s health was deteriorating.
Muddassar Arani also said Muslim inmates were not being given proper Halal food and she had raised the issue with the governor of Belmarsh.
The US accuses Mr Hamza of attempting to set up a terrorist training camp in the north-western state of Oregon and sending someone to Afghanistan to fight for the Taliban.
He is also charged in relation to a hostage-taking in Yemen in 1998, which left three Britons dead.
It is alleged he gave advice to the kidnappers by satellite phone.
Mr Abu Hamza’s lawyers argued he will not get a fair hearing in the US.
They say British police investigated him over the Yemen incident but no charges were laid.
The full hearing has been adjourned until 16 October.
If the court rules he should be extradited, the home secretary would then have to decide whether to order it.
Under current UK rules Mr Abu Hamza cannot be extradited to face execution overseas and any such sentence, if imposed, would not be carried out.
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