They didn't "break" it as such. It was more crappy cipher security by the luftwaffe & heer that kind of let them in (as well as some useful help from the Poles) and with that collection of information the key could be calculated from constants in messages such as "Heil Hitler". That said it worked unless you count the trouble with the U-boat system, referred to as "tunny" I think, that was regularly changed & updated.
Turings later work is actually more interesting - and the Welchman story is even more depressing than Turings.
PS British government - a half assed half baked apology for driving the guy to suicide or having him murdered after chemically castrating him is NOT OK, you fucking safe-spacing whiney snowflake hypocrites - I note his family got no compensation or recognition for what Turing was put through, but then that wasn't in the budget was it?