The American invasion of Grenada in 1983 (briefly discussed in Episode 92 "Nuclear Weapons"), is widely seen as the nadir in the UK-US special relationship post-Suez. In the days leading up to the invasion, Mrs. Thatcher strongly and emphatically opposed any US intervention in a country which had been a UK territory less than 10 years prior and still nominally recognized the Queen as their head of state. As late as the eve of the attack, as she dined with the American ambassador, the Prime Minister had no idea of American intentions - writing that there was "no reason to think that military intervention is likely to take place." It was only after dinner concluded that she was blindsided by a communique from Reagan informing he was strongly contemplating invasion. She hadn't even finished composing a response before another cable from Washington arrived around midnight London time - letting her know American Marines were landing in Grenada in a few hours. Reagan and the American foreign policy establishment had left Mrs. Thatcher and the Foreign Office completely out of the loop, vividly demonstrating with humiliating nonchalance their ability to act unilaterally without consideration of British interests.
Reagan's call to Mrs. Thatcher came around noon the next day, reaching her right before she set off for a "tricky debate" in the House of Commons. Its purpose was performative rather than informative - this is why it was recorded in the first place (a rare exception, as the practice of taping conversations in the Oval Office ended right along-side the Nixon presidency). Reagan hadn't been suddenly woken up in the middle of the night, nor was the Prime Minister hearing about the invasion from him for the first time. The barely-contrived excuses delivered with Reagan's penchant for overly-florid performance was the requisite diplomatic fig-leaf required.
[Edit: The date of the conversation in the post title is incorrect. The invasion and the conversation occurred on October 25th not the 23rd.]