Protesters have called for Vince Cable to ban all arms sales to Israel in the height of the conflict.
The pledge comes as the Government sold £8bn in arms and military goods to Israel.
Actor John Altman was among those who handed a letter to Vince Cable’s office in Twickenham, calling for him to ban the sale of all UK weapons and components to Israel and revoke all weapons licences.
He said: "I have been sickened by the extreme brutality of the Israeli regime in killing so many innocent civilians in Gaza and their destruction of homes, schools and medical facilities.
"It is shocking to learn that local MP Vince Cable is actually responsible for sanctioning UK weapons exports to Israel, which may well have been used in this current conflict."
Wendy Hatto, secretary of Twickenham and Richmond Amnesty Group, said weapons exported under the Business Secretary's remit went to some of most repressive regimes in the world.
The Hermes drone has been widely used during Operation Protective Edge, the ongoing Israeli military action in Gaza, to monitor Palestinians, pinpoint targets and guide in missile and smart bomb strikes, Ms Hatto said.
Ministers said they would not stop licensing military equipment to Israel outright because they believed the country had a "legitimate right to self-defence".
The contracts - mostly for cryptographic software and military communications, but also weapon parts - will be individually examined to ensure they are not being used for internal repression or the provocation of conflict.
Downing Street confirmed it was conducting the review after David Cameron gave his strongest comments yet on the crisis, saying the UN was right to condemn the shelling of schools as a "moral outrage".
Vince Cable said: "Both Nick Clegg and I agree that we should suspend export licences for military equipment that might be used by Israel in Gaza.
"We have been making this case inside Government but have not yet been able to get agreement for this position. I hope and expect that to change shortly."