"In recent years, Gaza's isolation has devastated the economy. The lifeline of food and fuel has become crucial and half of the population depends on UN food supplies," said Steve Hucklesby, Methodist Church Policy Adviser.
"Palestinians have a right under international law to receive essential humanitarian aid.
"We appeal to the UK and EU to exert pressure on Israel to ensure that the border crossings are kept open."
The Methodist Conference adopted a motion in the summer calling on Methodists to write to their MPs and MEPs to demand urgent action on the humanitarian crisis in Gaza and to pray for peace and justice for all God's people in the Holy Land.
The five-month ceasefire between Israel and Hamas was close to folding on Friday after nearly two weeks of deadly clashes between Israeli forces and Hamas militants.
"We must hope for progress on dialogue in the coming months," said Hucklesby. "The additional tension created by military incursions into Gaza makes this more difficult."
Israel said it was keeping its border crossings with Gaza closed, now for the tenth day running, to pressure Hamas, despite pleas from the UN, EU and numerous NGOs for the immediate resumption of humanitarian convoys into Gaza, where 80 per cent of the population is dependent on aid.
A UN statement said Secretary General Ban Ki-moon was "deeply concerned at the deterioration of the humanitarian and security situation in Gaza and southern Israel".
"Measures which increase the hardship and suffering of the civilian population of the Gaza Strip as a whole are unacceptable and should cease immediately", the Secretary General said according to the statement.
Philip Luther, deputy director of Amnesty's Middle East and north Africa programme, said, "Israel's latest tightening of its blockade has made an already dire humanitarian situation markedly worse.
"This is nothing short of collective punishment on Gaza's civilian population and it must stop immediately."