It cannot be denied that the brilliant minds at Bletchley park were necessary to the success of the code breaking. However, all of their work would've been null if they didn't have the money and resources to build or run the machines they needed. For this reason, the "brute force" was one of the most important factors to Allied success.
The Polish were the first to figure out a way to crack the enigma cipher. They were able to build the machines they needed to use brute force to decipher the messages. Everything was going great for them until the Germans added more elements to the Enigma Machine, meaning the Polish would've needed more machines to continue their processes. They simply didn't have the resources to make that happen. That's when they shared their findings with larger Allied forces. Bletchley Park was able to create all the machines necessary to continue cracking the codes, and had the manpower to run the machines as well.
Later on in Bletchley Park the intelligence was key to continuing to crack the codes, once the Germans fixed some of their "human error" mistakes, like repeating the day code. At this point, pure brute force was not enough to read the messages. Prior to this, though, brute force was the key element to deciphering the German messages.