The new UK coalition government is expected to say it has approved £19m of aid money for the UN operation in Gaza.
It is likely to be spent on medical equipment and basic food supplies.
The money had already been earmarked but the timing of the announcement, expected on Monday, is significant, BBC Gaza correspondent Jon Donnison said.
It follows heightened scrutiny of Israel's blockade of the Palestinian territory after an aid ship was stormed six days ago, leaving nine dead.
Meanwhile on Saturday, thousands of people protested in London and Edinburgh about the incident and Israeli soldiers said they had boarded another ship peacefully and did not meet any resistance on the Irish-owned Rachel Corrie.
Foreign Secretary William Hague has repeated his calls for an investigation into Monday's storming of the Turkish aid ship.
Mr Hague said: "We continue to stress to the Israeli government the importance of an investigation that ensures accountability and commands the confidence of the international community, and includes international participation."
He added: "We urgently need to see unfettered access to Gaza to meet the humanitarian needs of the people of Gaza and to enable the reconstruction of homes, livelihoods and trade. That is why we continue to press the government of Israel to lift Gaza's closure.
"I am also discussing these issues urgently with our international partners."
Israel says the flotilla the Turkish ship was part of was breaking a blockade put in force to prevent arms smuggling to Gaza.
It says it repeatedly said the boats would not be allowed to reach the territory.
The Metropolitan Police said about 2,000 people took part in Saturday's demonstration in central London but organisers put the number at 20,000.
The protest included a march from Downing Street to the Israeli embassy. The marchers arriving at the embassy in Kensington, west London, numbered around 1,000, BBC correspondent Greg Wood said.
Among the protesters was Sarah Colborne, 43, of the Palestine Solidarity Campaign, who was aboard the Turkish Mavi Marmara Gaza aid ship where the activists died.
She spent almost two days in Israeli custody before coming back to Britain.
Meanwhile, police said about 2,000 people took part in a demonstration in Edinburgh, through the city centre from The Mound to the US consulate via Princes Street.
SNP MSP Sandra White read out a message on behalf of First Minister Alex Salmond and the Scottish government.
It said: "The Scottish government condemns the Israeli authorities' actions that resulted in the tragic loss of life on the Mavi Marmara.
"We have added Scotland's voice to that of the wider international community in condemning it, and calling for the immediate lifting of the Israeli blockade of Gaza."
Correction 18 August 2010: The organisers of this demonstration informed us after initial publication that we incorrectly attributed the number of 5,000 to them and that they had said 20,000 people were present.