Frankly they had the same freedom to ignore the invasion of Poland. They had a similar treaty with Czechoslovakia that they shrugged off. People overestimate the importance of treaties, nothing forces a country to honor an agreement and there are countless episodes in history where treaties were ignored. The Ottomans had a famous habit of ignoring and reneging agreements they made with various European powers that they justified with a principle from the Hanafi School of Islamic Jurisprudence that allowed Muslims to break agreements with the infidel if they threatened the Umma. There are also plenty of times where treaties were ignored without the need for any justification.

The UK and France declared war on Germany using their treaties with Poland as a justification, but the real reason was the realization that they were next. There was little that could have prevented France being dragged into the war as Germany had explicit plans for carving up French territory and the French had been the most aggressive pushers of punitive measures being placed on Germany. The British elites probably appreciated that letting France fall would have lost them their only reliable ally on the continent (before people tout the Anglo-Portuguese alliance I said reliable, France was a major power Portugal was not) leaving Germany, a bitter rival, in charge of Europe.

The real question is why the French and British didn't ally with Germany since they actually agreed on many fundamental points. All three held no love for Jewish people, the British elites in particular agreed with the German notions of Nordic white supremacy, and the British and Germans in particular along with the French to an extent felt threatened by Soviet Communism...a concern shared with the United States.

This seems more like a question for /r/HistoryWhatIf. I doubt the people here will speculate on a question like this.

Sorry, but your submission has been removed because we don't allow hypothetical questions. If possible, please feel free to rephrase the question so that it does not call for such speculation, and resubmit Otherwise, this sort of thing is better suited for /r/HistoryWhatIf.