So, this is a question that could have whole books written in response, but I'm going to focus on two points:

Re: Abwehr secret agents. Due to the Double Cross System, by the time planning for the D-Day invasion was underway, every single German agent in Britain was under the direct control of British Intelligence. Either they were captured and turned into double agents, captured and imprisoned with British intel imitating them, or dead.

At least 62 Abwehr and Sicherheitsdienst (SD) were captured/turned/controlled by Double Cross. This was partly due to the fact that the Germans didn't give good (by modern standards at least) attention to providing their agents with appropriate cover, training, or equipment. For example, on agent, code-named SUMMER, sprained his ankle on parachuting into Britain, and aroused suspicion when he hobbled into the nearest town wearing a completely out of place smart blue suit.

There were exponential results as fresh agents were instructed by their handlers to contact those already established (who were, unbeknownst to the High Command, already compromised). Of course, real intelligence would have to be included with the fake information in order to not raise suspicions, which was a delicate balancing act that was masterfully handled. For example, real intel on Operation Torch, the invasion of North Africa, was sent with a postmark prior to the invasion, but British authorities delayed its delivery until after the invasion. It was militarily useless upon arrival, but demonstrated "good faith" by the spy in question, bolstering their bona fides.

The Germans had zero reliable intelligence aparatus in the UK. Garbo, a "german spy" in Portugal was the most prolific of these operatives. He was in reality more of a conman, who developed an entire phantom sub network of agents (existing only in his head), charging the Germans for the requisite funds to keep his "network" afloat. He eventually approached the British and became an official disinformation agent.

You may have also heard of Operation Mincemeat, where a dead body was dressed up as a British intelligence officer and fake documents were planted on his corpse before it was released at sea where the Germans would find it once it washed up on the shore. Double Cross was an unparalleled intelligence success, unmatched in modern history.

Operation Fortitude (a subset of Operation Bodyguard) was a massive deception project involving artists, makers, painters, etc, developing entire fake armies, complete with inflatable tanks, landing craft, radio traffic, etc, for the purpose of misleading Germany about the location of the invasion.

Any one of these operations could realistically be considered to be massive intelligence coups, but when they were all combined, it was a massive undertaking that's truly unparalleled in intelligence history. In fact, Christopher Andrew, in his excellent history of MI5, writes that the British disinformation success was so staggering in its scope & complexity, that the risk after the war was that politicians would expect similar successes as standard, quoting Guy Liddell of MI5 as saying "Our main difficulty may not be so much to persuade senior officers to allow us to run double-agents, but to prevent them from making us run everything in sight as a double agent."

References:

Double Cross by Ben Macintyre

Defend The Realm: The Authorized History of MI5

Further Reading for the interested layman:

• https://en.wikipedia.org/wiki/Juan_Pujol_Garc%C3%ADa
• https://en.wikipedia.org/wiki/Double-Cross_System
• https://en.wikipedia.org/wiki/Operation_Fortitude
• https://en.wikipedia.org/wiki/Operation_Bodyguard
• https://en.wikipedia.org/wiki/Camp_020