If Great Britain entered the war to protect Poland from Hitler why did they end up leaving it under Stalin's rule after the war?

This is not quite correct. The Franco-British commitment to Poland was not a military alliance with Poland per se. The alliance was directed specifically at Germany to check German aggression. The Anglo-French alliance may have went to war in 1939 in response to Germany's invasion of Poland, but they did not go to war for Poland. The Polish alliance was more about drawing a line against Hitler's expansionism than it was about protecting the rights of Poland. This was why neither Paris nor London declared war on Stalin in the wake of the Soviet invasion of Poland. With the exception of a few outliers, most Anglo-French decisionmakers tried a sort of constructive engagement with Stalin in the hopes that the nascent German-Soviet partnership would founder because of the mutual antipathies between Hitler and Stalin. Anglo-French leaders may have paid lip-service to the Poland's freedom and hosted the Polish government-in-exile, but Poland was still a chip, not a partner in Allied calculations.

The low priority placed on Poland goes a good way to explain the postwar position of Eastern Europe. The Red Army in 1945 was strong enough to pretty much impose new borders and friendly governments by force if necessary. The Soviets had boots on the ground in Eastern Europe and Anglo-American diplomats knew this. Negotiations at Yalta and later Potsdam were tense, but there was realistic assessment that this was a region of the world where the Soviets already had a preponderance of military power. Short of war, there was relatively little that the Anglo-Americans could do to rectify this situation. The Anglo-American dilemma was that in order to keep Stalin involved in diplomacy for both the war against Japan and the postwar period, they had to sate these immediate territorial demands. The Anglo-American response to Soviet territorial aggrandizement has attracted more than its fair share of critics both at the time and since. Notions of the "betrayal at Yalta" were quite common in Eastern European emigre groups as well as various anticommunist ideologues during the Cold War. While some of this critique has a point, the postwar Soviet occupation did lead to dictatorships, it can go too far. Eastern Europe lay very low on the list of priorities for Anglo-American diplomats and leaders. Not only had their participation in the Axis cost them in terms of prestige, there was a sense among some Anglo-American opinion that Eastern Europe was the natural sphere of influence for Soviet power. One example of this was that the emigre former head of the Russian 1917 Provisional Government Alexander Kerensky actually argued in editorials and letters in 1944/45 that Soviet aggrandizement in the Baltic was a natural redress of the First World War. Even though Kerensky was no fan of Stalin or the USSR, he was a proponent of expansion. So charges of betrayal often project a sympathy for Eastern Europe that just was not present among Anglo-American leaders.

The other problem with the betrayal charge was that there was no real viable option to dislodge the Soviets from Eastern Europe to restore the 1939 borders. Stalin knew the Red Army gave him a valuable card and he pushed his advantage. Refusing to acknowledge these borders and new governments was a quixotic task and could lead to a darker road of a renewed war. Such a prospect was not one any Anglo-American leader relished and even the least-worst option of diplomatic isolation and non-recognition of the Polish satellite state had the potential to spiral into another conflict.