Just backing up what /u/Kynas said here's an article from the New Yorker, "Trust No One: Kim Philby and the hazards of mistrust" which covers the effects within British Intelligence of Kim Philby being discovered to be a spy. Much better than the average article of that type. The New Yorker is paywall-free for a couple of months but after that you'll have to pay or register .. I think.

I was interested the degree to which what's written in that article resonated with the plot of the John Le Carre novel "Tinker, Tailor, Soldier, Spy" which is clearly referring to the same events but to a much greater degree than I had previously realised.

It certainly damaged US confidence in British intelligence for a time — partly because Philby was one of the most senior counterintelligence officers in Britain, and worked closely with James Jesus Angleton, the father of counterintelligence in the CIA. The two developed a close working relationship and friendship, and although Angleton didn't speak publicly about his feelings on Philby after he was revealed as a Soviet agent, one suspects he must have felt betrayed.

The unmasking of the first three of the Five also came little more than a year after the arrest of atom spy Klaus Fuchs, which had already dealt a blow to the relationship between British and US intelligence. When you also consider that this period was at the height of FBI director J. Edgar Hoover's power, and his known obsession with internal security and deep (and justified) conviction that there were Soviet spies everywhere, the situation was decidedly embarrassing for the British.

American confidence in British intelligence would also have been affected by the fact that three of the Cambridge Five (Philby, Guy Burgess and Donald Maclean) had been stationed in Washington while working as Soviet agents. This was not just a British scandal; for US intelligence, it cut close to home. Philby, in particular, also had access to the VENONA project — at the time, the crown jewels of American SIGINT — and is known or suspected to have used that access to warn Moscow that US-UK intelligence had uncovered several of their atomic spies, including Klaus Fuchs, and to have warned Burgess and Maclean that they were under suspicion, thus enabling their successful defection.

Christopher Andrew has some good detail on the impact of the 'Magnificent Five' on the special relationship, in his history of the Security Service:

The [MI5 director-general Percy] Sillitoe flew to Washington to brief, and attempt to mollify, the irascible J. Edgar Hoover in person. As well as undertaking the difficult task of trying to reassure a skeptical Hoover about the current state of British security, he quickly found himself caught in cross-fire between the [FBI] and the CIA. Hoover was affronted that the [Director of Central Intelligence], General Bedell Smith, had learned from British liaison of the existence of the VENONA decrypts which identified Maclean as Agent HOMER. Though Hoover had been content for MI5 to have access to VENONA, he was determined that the supposedly insecure CIA should not.

But how much long-term damage it did to the relationship is hard to say; certainly it didn't cause irreparable harm. The US-British intelligence alliance represents one of the closest collaborations between two foreign intelligence agencies in history. Among other things, the traumatic experience of discovering that the British intelligence and diplomatic services had been so effectively penetrated during the 1930s, 1940s and 1950s galvanised the British intelligence community to make counterintelligence a long-term strategic priority. The Security Service are (still) regarded as domain experts in CI. This is also from Andrew's history of the Service:

A retrospective analysis of Service counter-espionage in the later Cold War concluded:

[...] The defensive system that we developed over the years put enormous pressure on hostile [intelligence officers], most of whom felt apprehensive and intimidated before they even arrived here, such was our reputation.

I wrote a long answer to a question on intelligence history yesterday, so will copy and paste my notes on the historiography in this field:

In terms of broader reading in this area: Britain currently has several of the world's leading intelligence historians, so there's been a lot of excellent scholarship on British and Soviet intelligence history published in the last twenty or so years. In the texts below, you'll find a huge amount of information on the intelligence war before and during the Second World War, and then throughout the Cold War.

As well as the Aldrich history of GCHQ, there are also recently-published official histories of the other two British intelligence services, written by professional historians who were given unprecedented access to the services' archives:

• Keith Jeffery, MI6: The History of the Secret Intelligence Service (2010)
• Christopher Andrew, The Defence of the Realm: The Authorized History of MI5 (2009)

On the Soviet side, Andrew has written several important histories of the KGB, working with two of the most senior Soviet intelligence officers to defect to the west — Oleg Gordievsky and Vasili Mitrokhin. They're excellent reads, and incredibly informative on the history, practice and thinking behind Soviet intelligence during the Cold War:

• Christopher Andrew & Oleg Gordievsky, KGB: The Inside Story of its Foreign Operations from Lenin to Gorbachev (1990)
• Christopher Andrew & Vasili Mitrokin, The Sword and the Shield: The Mitrokhin Archive and the Secret History of the KGB (2000)
• Christopher Andrew & Vasili Mitrokhin, The Mitrokhin Archive II: The KGB and the World (2005)

Those histories of the KGB cover the recruitment and operations of the Cambridge Five in exhaustive detail — in fact, the 1990 history by Andrew and Gordievsky was the first to publicly confirm the identity of the 'Fifth Man' as John Cairncross.

Edit: an important note about the Jeffery history of SIS — it's an excellent piece of scholarship, but it's a history of the service from 1909-1949 (because they declined to give him access to the archives post-1949.) So it's excellent on the two world wars, and very useful on the context and conduct of the early Cold War, but does feel like it ends rather abruptly just when things are starting to get interesting. For your particular question, I'd suggest also consulting Richard Aldrich's The Hidden Hand: Britain, America and Cold War Secret Intelligence (2006) and Philip H. J. Davies' MI6 and the Machinery of Spying (2004).

Well, I just finished reading Peter Wright's "Spy Catcher" and his assessment of the situation was that it caused significant distrust of the UK system by the US. He indicates that at one point the CIA basically stopped bilateral intelligence sharing with MI5/6. Moreover, the CIA would take all the intelligence the UK could muster, but gave very little in return. This went on for some time, until well after Wright left service. Mainly, because I think the US, at the time, (and Wright did certainly) suspected that Roger Hollis (the DG) was in fact a KGB operative.