The ban on Palestine Action has created a “culture of fear” among those campaigning for Palestinian rights and judges were right to deem it unlawful, the court of appeal has heard.

Shabana Mahmood is challenging the high court’s decision in February that Palestine Action’s proscription, the first of a direct action protest group, represented a “very significant interference” with the rights to freedom of speech and assembly. It also found that the ban, which remains in place pending the appeal, was a breach of the home secretary’s own policy on proscription.

On Tuesday, Sir James Eadie KC, representing Mahmood, said in written submissions that the high court’s conclusion that the ban’s interference with human rights outweighed the importance of proscribing the group was “overstated and wrong”. He also told the court of appeal that it did not breach her policy, which gave her “broad discretion” on counter-terrorism and was not intended to “straitjacket” her.

In his submissions, Raza Husain, representing Huda Ammori, co-founder of Palestine Action, said: “The consequences of [Palestine Action’s] proscription are severe. It has caused – as intended – the total destruction of a protest group with considerable popular support, which seeks to prevent atrocity crimes by Israel against Palestinians, while those crimes are ongoing and extensive.

“It has also given rise to severe restrictions on the fundamental free speech and assembly rights of vast numbers of people which have been curtailed and chilled in relation to a matter of current, critical importance.”

He told the court that the ban, the first based on serious damage to property, had created a “‘culture of fear’ among those campaigning for Palestinian rights” with individuals and organisations self-censoring and refraining from lawful advocacy.

He added that police had been “surveilling, stopping, questioning, and arresting pro-Palestine protesters (often based on an erroneous understanding of the legal consequences of proscription), regardless of whether the individuals in question have any association with PA (for example, simply for wearing keffiyahs, or clothing or insignia indicating solidarity with Palestinian people)”.

Husain said the home secretary should have considered less restrictive alternative measures to combat Palestine Action and taken into account that Elbit Systems UK and other organisations PA targeted were “alleged to have been involved in serious criminality” in relation to Israel’s assault on Gaza

Eadie said: “Whilst no doubt some people would self censor and the restrictions imposed by the criminal offences were significant to the extent of their specific scope, the divisional [high] court failed to accord proper weight to parliament’s decision that a fixed suite of criminal offences were the consequences considered to be both effective and appropriate in the context of proscription.”

Since proscription, more than 3,000 people, whose fate rests on the outcome of the appeal, have been arrested under the act for holding placards saying: “I oppose genocide, I support Palestine Action.”

Eadie said: “Persons expressing support for, and associating with, PA should not have been treated [by the high court] as undertaking peaceful protest; rather, they were supporting a terrorist group, the activities of which were inconsistent with democratic values and the rule of law.”

He told the court that the fact that individuals might commit offences under the Terrorism Act that did not themselves meet the legal definition of terrorism had been contemplated by parliament, which intended that “proscribed organisations are deprived of the oxygen of publicity and support”.

He added: “It ​remains open to people to support the Palestinian cause, to protest against Israel’s actions in Gaza.”

The hearing is being overseen by a panel of five judges (instead of the usual three), led by the lady chief justice. It is expected to conclude on Thursday, when proceedings will be in private, with judgment reserved until a later date.