In central London, protesters - including the singer Annie Lennox and former mayor Ken Livingstone - marched along the Embankment to Trafalgar Square. Some chanted "Free, free Palestine" and "Israel terrorists".
Many stopped en route to throw hundreds of shoes at the gates of Downing Street, echoing the protest of an Iraqi journalist who threw his shoes at President Bush last month.
Lyndsey German, of the Stop the War Coalition, said the protest was "just the start of the campaign".
"If there is an invasion of Gaza, as looks likely, by the Israeli army, if the blockade continues with people suffering from shortages of food and medicine, then I think this will grow," she said.
Tens of thousands of Israeli Arabs earlier staged a protest in the northern Israeli town of Sakhnin about the bombing raids on Gaza.
The protest in Sakhnin was one of the biggest by Israeli Arabs in 10 years
Demonstrators waved Palestinian flags, and chanted slogans denouncing Israeli leaders, including "Gaza will not surrender to the tanks and bulldozers" and "Don't fear, Gaza, we are with you".
Following a minute's silence, Sakhnin mayor Mazen Ghanaim said the Israeli military was "committing crimes in Gaza before the eyes of the international community", but also called on militants to stop firing rockets into Israel.
One Israeli Arab politician, Jamal Zahalka, said it had been the biggest demonstration by Israel's Arab minority in the past 10 years.
There was also a large protest by Palestinians in the West Bank city of Hebron.
Israeli air and naval forces continued to bomb and shell targets in the Gaza Strip on Saturday. One person was killed as large parts of the American International School in the north-western town of Beit Lahiya were destroyed.
Palestinian militants meanwhile fired more rockets into southern Israel
Israeli artillery later fired dozens of shells into the east of the territory, witnesses and Palestinian media said.
Palestinian militants meanwhile fired more rockets into Israel. One rocket hit the second largest port, Ashdod, 30km (19 miles) from the border with Gaza.
Maj Avital Leibowitz, a spokesperson for the Israel Defence Forces (IDF), said the offensive would continue until Hamas stopped its attacks. Four Israelis have been killed so far by rockets fired by militants in Gaza.
"From the beginning of this day, the eighth day of the operation, the air force and the navy have attacked 40 different targets. The targets are of course Hamas-affiliated," she told the BBC. "The school... was a site for launching rockets."
The Israeli government has also threatened to launch a ground offensive on Gaza. It has called up army reservists, and tanks and troops are massed on the frontier.
BBC Middle East Editor Jeremy Bowen says a week of bombardment has not been able to stop militant rocket attacks, and Israel now has to decide whether to send in ground troops.
But in a pre-recorded statement broadcast on al-Jazeera TV, Hamas political leader Khaled Meshaal said Israel would be making a "foolish mistake" if it did.
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