From what I understand British intelligence did a pretty good job during World War II but are there any instances where they had big failures with noticeable consequences?
From 1942 to 1944, the SOE intelligence network in the Netherlands was run by the Germans, under Operation North Pole, also known as the Englandspiel in German. English-trained Dutch intelligence agents were parachuted into Holland, where they were captured by the Germans. These agents were forced to broadcast messages the Germans gave them. When new agents were parachuted in, they would meet up with the captured agents, and be captured in turn. SOE managed to completely miss the warning signals the agents hid in their messages. When two of the captured agents managed to escape to the UK, they were ignored, as German intelligence had planted messages claiming that they were actually German double agents. This didn't have any major effect on the war as a whole, as SOE agents were more saboteurs than spies, but is one of the more serious failures of Britain's intelligence agencies.
The battle of Crete was lost in no small part because British intelligence had informed General Bernard Freyberg that based on Enigma intercepts the German glider insertion was a feint and the main invasion force would be coming from the sea. This caused him to keep more assessts on the beaches defending against an attack that never came. By the time he realized the paratroopers were the main effort the Germans had consolidated their position and pushed allied forces on to the beaches and the island fell.