For 10 months, Britain’s Conservative government had moved almost in lock step with the United States in its response to Israel’s war in Gaza. Now, under its new Labour government, Britain is edging away from its closest ally on the conflict. By the end of this week, Prime Minister Keir Starmer is expected to drop the previous government’s objections to the International Criminal Court prosecutor’s pursuit of an arrest warrant for Prime Minister Benjamin Netanyahu of Israel, two people briefed on the government’s deliberations said. Taken together, these steps show a government that is willing to pile more pressure on Mr. Netanyahu for Israel’s harsh military response in Gaza. It also shows that Mr. Starmer, a former human rights lawyer, is paying more heed to international legal institutions than the United States.