The simple answer is that they didn't really want another enemy when they already had their hands full with Germany.The treaty signed between Britain and Poland guaranteed Poland protection from any outside aggression, and so the British and French should have declared war, but with Poland almost finished off, there was no reason to antagonize the Soviets in order to uphold what was about to become an irrelevant treaty. The Soviets were the biggest military power in Europe at the time and Britain and France knew they couldn't afford to push the Soviets further into Germany's arms. It should also be noted that Chamberlain followed a pretty consistent "Germany first" strategy, that is he wanted to deal with the threat of Germany, before any other threat. That is why Chamberlain paid so little attention to the Japanese aggression in China, or the Italian aggression in Africa and the Balkans. So even if the British and French wanted to declare war on the Soviets, they would have waited until after Germany was dealt with.

In the case of Finland the western allies were planning on sending aid, and they did condemn the invasion. Britain and France had a plan where they would send aid to Finland but along the way stop in Norway and Sweden to seize the important iron ore mines in Northern Sweden and the important ports of Norway. It was hoped that such a large allied force landing in their country would force the two countries to join the allies. Once those two countries had joined the allied expeditionary force could aid the Finns. However, Finland signed a peace treaty with the Soviets and the plan was scrapped despite being very popular among the military establishments of Britain and France.