The first casualty of that declaration was not German—but the British ocean liner Athenia, which was sunk by a German U-30 submarine that had assumed the liner was armed and belligerent. There were more than 1,100 passengers on board, 112 of whom lost their lives. Of those, 28 were Americans, but President Roosevelt was unfazed by the tragedy, declaring that no one was to "thoughtlessly or falsely talk of America sending its armies to European fields." The United States would remain neutral.
As for Britain's response, it was initially no more than the dropping of anti-Nazi propaganda leaflets—13 tons of them—over Germany. They would begin bombing German ships on September 4, suffering significant losses. They were also working under orders not to harm German civilians. The German military, of course, had no such restrictions. France would begin an offensive against Germany's western border two weeks later. Their effort was weakened by a narrow 90-mile window leading to the German front, enclosed by the borders of Luxembourg and Belgium—both neutral countries. The Germans mined the passage, stalling the French offensive.
The containment of the Soviet Union depended upon the credibility of NATO and its forces. The Soviet Union imploded as our containment policy worked. If the Russians don't believe that NATO's commitment is real, then there is a real danger of war. And unlike 1939, both sides have nuclear weapons.
And I believe Poland can go toe-to-toe with Russians on their home turf. I think their soldiers are more professional, than the Russian conscripts, and they are definitely more motivated.
The ironic part is that by doing this, the French and English brought hell on themselves -- the German General Jodl pointed out that there were only 23 divisions of German troops on the west opposed by something like 110 divs of French and English. The French tanks and artillery were actually better than the German.
If the French and English had actually attacked Germany instead of just talking, they would have ended the war in 1939 and saved millions of lives -- a lot of it their own.