The Brits didn’t break Purple, they weren’t even working on Purple. It was part of the division of effort between the US and the UK.
And while we knew the IJN carriers were at sea, we didn’t know where they were or where they were headed. The fleet was under radio silence, so traffic intercepts didn’t help.
We did intercept a transmission from a destroyer that had been an escort to one of the carriers. The destroyer was in the South China Sea, from which the USN presumed that the carriers were heading for Singapore.
There was zero evidence that suggested Pearl.
Family was in the escort for the Enterprise, just outside of Pearl. On patrol from October 1941 with weapons free against any japanese ships (they still had the orders from when leaving Pearl). They always said the Brits knew what was going on, and they were in the chain of command to know this, no matter what code (which they always referred to-as they were eyes only on the intercepts).
So many historians give FDR a “pass”—because they could not get through the coverup FDR did when he trashed Kimmel and Short (when in fact FDR, and don’t forget the existing Soviet spies in his cabinet even then- was setting up Pearl for failure. Deliberately). And this clown is a hero of joey bags xiden and all the “progressive” clown democrats, all of them machine politicians. American socialists pitted against Euro socialists (same as now).