Leo Seelig, prosecuting, told the court that the Crown Prosecution Service would be arguing that the four men should be sentenced on the basis that the arson attack was related to terrorism.
Mrs Justice Cheema Grubb said she would not rule on the question of terrorism at this stage – with defence counsel arguing that there was no evidence for such a connection.
The judge said that the four would be sentenced following the outcome a trial of a fifth man, Subhan Ahmed, who has denied assisting an offender.
Iqbal and Khan, of Leyton, Atshatshi, of Dagenham, and Ali, of Walthamstow, were remanded into custody.
Run by volunteers, Hatzola has served the north London community of Golders Green, which has a large Jewish population, since 1979.
Hatzola, the Hebrew word for save or rescue, is a large non-profit, Jewish-led organisation that provides a free emergency medical response and transportation to hospitals regardless of faith by volunteer medics.