This question has numerous possible answers. An entire Israeli historiography debate is structured around aspects of this question as a component of the 'Official History vs New Historians' argument. I believe that Oxford Historian Avi Shlaim would probably argue that the aftermath of the Holocaust played a significant role in the British pushing for an independent Israel as more compelling than their desire to withdraw from a growing Jewish insurgency and domestic Arab civil unrest in the Mandate territory. Former Ben Gurion University of the Negev professor Benny Morris, who wrote quite substantially about the events surrounding the independence struggle in his book 1948 took a similar stance that the British were amenable to supporting a Jewish-led independence of the Mandate and supported it at the UN.

As a historian myself, I vehemently disagree. The insurgency played the deciding factor in British withdraw, and continued unabated until total withdrawal of British forces had occurred. Even still, the British assisted the Arab forces with aerial reconnaissance and several air engagements with Israeli forces occurred over the Sinai peninsula. Britain did not even extend legal recognition of Israel until 1950, two years after Israeli independence was made legal by the UN.

As for the UN and the international community's role in creating Israel, and regarding the impact of the Holocaust. There are many perspectives on this, both within Israeli academia, among other historians, even international Jewish leadership. Nahum Goldmann, former President of the World Jewish Congress, famously said that "Without Auschwitz, there would be no Israel", for example. I personally argue that the efforts of Zionist political leaders and military efforts of the Urgun, Lehi and Haganah militias led to the creation of Israel. What the Holocaust did was garner international sympathy for the Jewish cause and facilitate a greater contribution of resources to those Zionist leaders to more effectively pursue independence.

My argument, and one taken by other academics such as Bundeswehr University Munich professor Michael Wolffsohn in his 1993 article Eternal Guilt? Forty Years of German-Jewish-Israeli Relations, is that the Holocaust served as a multiplier for the Jewish cause and provided the resources necessary for early Israeli state survival, but did not directly or solely lead to the creation of Israel. Independence was obtained through political and military means by the Jewish people over several decades.