Luke's summary omits details. McGrayne does indeed cover the Polish efforts, and then about the British efforts:

According to Frank Birch, head of the GC&CS naval intelligence branch, superior officers informed him that the “German codes were unbreakable. I was told it wasn’t worthwhile putting pundits onto them. . . . Defeatism at the beginning of the war, to my mind, played a large part in delaying the breaking of the codes.”7 The naval codes were assigned to one officer and one clerk; not a single cryptanalyst was involved. Birch, however, thought the naval Enigma could be broken because it had to be. The U-boats put Britain’s very existence at stake. Turing had still another attitude. The fact that no one else wanted to work on the naval codes made them doubly attractive.

... codebook had to be “pinched,” as Turing put it. The wait for a pinch would stretch through ten nerve-racking months. As Turing waited desperately for the navy to get him a codebook, morale at GC&CS sank. Alastair G. Denniston, the head of GC&CS, told Birch, “You know, the Germans don’t mean you to read their stuff, and I don’t expect you ever will.”19

...A second bombe incorporating Welchman’s improvements arrived later that month, but the fight for more bombes continued throughout 1940. Birch complained that the British navy was not getting its fair share of the bombes: “Nor is it likely to. It has been argued that a large number of bombes would cost a lot of money, a lot of skilled labour to make and a lot of labour to run, as well as more electric power than is at present available here. Well, the is- sue is a simple one. Tot up the difficulties and balance them against the value to the Nation of being able to read current Enigma.”21