Al-Haq supporters held a press conference outside the High Court
Palestinian human rights activists are suing the UK government for alleged "flagrant" breaches of international law in its dealings with Israel.
The organisation Al-Haq has called for a High Court judicial review into the UK policy of selling arms to Israel.
It says Britain broke international obligations not to render "aid or assistance" to Israel following its invasion of Gaza last year.
The Foreign Office said Britain's arms trade was tightly regulated.
Al-Haq said the UK government appears to have "positively assisted" Israel in its invasion of Gaza last year by continuing to sell it weapons.
The organisation also says a record amount of UK arms exports to Israel were approved in the first quarter of last year.
Following the lodging of papers in the High Court calling for a judicial review, Phil Shiner, a solicitor representing Al-Haq, said he believed the issue deserved a full court hearing.
He said: "It is Al-Haq's position that if the UK were to meet its international obligations now, Palestinian lives and limbs in Gaza would be saved.
"There would be a much greater chance of accountability for Israel's actions and a change in the policies of all key players so that nothing like it can ever again befall the Palestinian people."
Al-Haq's case is that Britain has an obligation, under international law, not to assist Israel because it says Israel has interfered with the Palestinian right to self-determination, has acquired territory by force and has committed war crimes.
Other pro-Palestinian groups have voiced support for the legal action.
Bruce Kent, vice president of the Catholic peace group Pax Christi, said: "This government is complicit in arms sales to Israel some of which have been used to commit war crimes."
The Foreign Office said it believed the claims made on behalf of of Al-Haq were "wholly inapt" for resolution in a domestic UK court.
In statement it said: "As a matter of policy, the government continues to work hard in an effort to secure peace in the Middle East.
"From the outset of the recent conflict the government worked around the clock to achieve an immediate ceasefire."
It said the UK helped broker a ceasefire at the UN Security Council, and that the UK supported investigations of what it termed "credible allegations of war crimes".
The statement added: "Britain has some of the tightest regulations in the world for arms sales.
"The government monitors the situation in Israel with care in considering applications for arms export licences."
The increase in arms sales to Israel last January, it said, was due to the approval of a single licence for "high value naval communications equipment".