WWI was not the first time the idea was first floated to the British government and taken seriously at all. As early as 1902, Joseph Chamberlain was negotiating with Theodore Herzl on whether areas like the Sinai or el-Arish were viable locations for a Jewish state. He even offered a plateau in Nairobi, which was ultimately nixed as a plan.

This thread goes into more detail on those plans.

In 1903, there were many doubts a plan could happen, since Chamberlain resigned.

Even before all of this, Herzl had attempted to negotiate with the Ottomans on a state in Palestine, and garnered the support of the Kaiser, and that was in 1898 or so.

There were attempts before WWI, and the Europeans had given it support along the way. There were attempts even earlier, but those were far less likely to succeed, and taken far less seriously. Some attempts reach as far back as the 1860s, if memory serves. One notable is that by Moses Hess (a German Jew), who wrote in Rome and Jerusalem that a Jewish social commonwealth in Palestine would be a solution.

There are indeed indications that this was meant to be a "mutually beneficial agreement", in that there would be a way to get rid of the Jews in Europe while at the same time giving them a state. In 1925, Lloyd George (instrumental in passing the Balfour Declaration, since he was Prime Minister at the time) told a Jewish audience that "acetone converted [him] to Zionism". Here, he's referring to Weizmann's acetone production method that was far more economical, and pointing out that it was not some moral consideration that made him believe in the idea of a state. It was both a dislike for the Jews (what Sir Mark Sykes termed the "hybrid type of assimilating Jew" and their "power/influence/wealth") and gratitude for Weizmann that made the decision to pass the Balfour Declaration, the first real "commitment" of any sort to help the Jews get anywhere in Palestine (debatable as a commitment, but still very important in history). As a sidenote, Sir Mark Sykes was a prominent diplomatic advisor.

To be fair, there were many (including those above) who gave other statements about how they believed Jews had the best right to Palestine, etc. However, it's still clear that the beliefs were not mutually exclusive, and that they could be convinced by the benefits of solving "The Jewish Question", by the contributions and hard-work of Weizmann, and by the belief that they were taking a morally justified position.

Sources:

Reich, Bernard. A Brief History of Israel. New York, NY: Facts On File/Checkmark, 2008. Print.

Joe Stork. Understanding the Balfour Declaration MERIP Reports, No. 13 (Nov., 1972), pp. 9-13

Jacques Kornberg. Theodore Herzl: A Reevaluation The Journal of Modern History, Vol. 52, No. 2 (Jun., 1980), pp. 226-252