There's an actually story from the Cuban Missile Crisis that nearly resulted in a false retaliation strike. Prior to the Crisis, Military thinking was that Soviet attacks would come over the Arctic and most stations in the United States faced the North Pole. Naturally, when missiles were discovered in Cuba, a lot of early warning systems were hastily pointed the other way, including one in New Jersey. During the 13 days of the Stand off, the newly southern facing center got news they really didn't want to recieve... there was a launch from the general Cuba area of a missile... or what looked like a missile until a few tense moments showed that it's course would take it too high and towards West Africa... as it turns out, the "missile" was actually a Rocket launched from Cape Canaveral... no one had told the egg-heads at NASA that now's not the time to be launching rockets... Just one of four events in the Cuba Missile Crisis that threatened to unleash all out nuclear war, but speaks a lot for your question.
Incidentally, during the Cold War, especially the 80s, it was believed that Soviet Missiles would expend a total of 4 minutes from launch to impact anywhere on the British Islands (Compared to United States, where this time was about a 30 minute window from Launch to Impact) so the British Second Strike (the retaliation, and under MAD, the defensive part of having nukes) was not thought to be an immediate response. Rather, their Nuclear Subs were required to check a series of automated signals. If they could not confirm the signals, they were to open the "Letters of Last Resort" and follow the instructions. These letters were written by the Prime Minister, sealed in envelopes and placed in safes in each of the 4 nuclear subs in the British Navy. These letters contained the final instructions of the British Government should the worst happen. Because the policy is to destroy all Letters of Last Resort after the end of a PM's Premiership, we do not know the specifics of the types of orders given, but speculation ranges from which cities to target for retaliation (presuming they still stand) to which nation to take future orders from.
The signal is assumed to have a number of redundancies both fore maintenance, breakages, and survival of some of British Government outside of London, so the destruction of London would likely not entail retaliation from the British.
Though depending on the year, the political situation would dramatically shift. One important thing to consider is November 1983, when the television film "The Day After" aired in the U.S. Although it admitted that the story was a very optimistic outlook on the challenges facing the United States after full scale Nuclear War, the film was grim enough to scare even Ronald Regan into rethinking Nuclear Policy and convinced him to de-escalate the situation. It combined with the U.S. Realization that the Able Archer '83 exercise had put the Soviet Union on such a high alert that it's considered the closest humanity ever came to an intentional Nuclear War that didn't involve Cuba for a one two punch to get the two sides talking. Though debatable about who sent the message, the film's producer, Nicholas Meyer, did get wind that the film had a great deal of influence behind the push for the INF Treaty of '88.
Because of this, the late 80s had a bit more cooperation with it than the early 80s and by George H.W. Bush's Presidency, relations with the Soviet Union had smoothed out. The U.S.S.R. collapsed on Christmas Day, 1992, rather peacefully, and the 90s era of the U.S.S.R. military was categorized by a lot of budget problems leading to a rather inefficient war machine. The threat of Russian Nukes at this time was more from the fact that so many of the U.S.S.R. nukes went missing during this period.
Of course, if you noticed a few paragraphs back, I said Intentional Nuclear War, I wasn't kidding. The larger threat is equipment malfunctioning and behaving as if there were inbound targets when there were not. In the moment, these false alarms would have likely triggered an all out Nuclear Exchange if not for some quick thinking. In 1979, NORAD computers experienced an error when they detected a full scale launch from the USSR inbound from the states. Retaliation orders were prepped, but the panic was called off when early warning radar failed to confirm any inbound missiles. As they discovered, the alert was tripped when a training scenario for the system was allowed to play on the live data systems by mistake. Here, disaster was averted because, despite a launch detected, there was nothing inbound.
In another scenario, one man literally saved the world when Lt. Commander Stanislav Yevgrafovich Petrov was on duty and the Soviet Early Alert system reported that five U.S. Minute-Man missiles had been launched and were inbound to the U.S.S.R. Again, his staff had a panic moment, but Lt. Cmd Petrov spotted the problem, namely, that there were only five missiles inbound, and pointed out that any U.S. First Strike would be massive... Five missiles to destroy the whole of the Soviet Union was not how the United States would start a nuclear war. Coupled with the fact that the satellites involved were new and there were possible buggy problems, he declared the incident a false alarm. His hunch was confirmed to be caused by some bizarre atmospheric conditions and sunlight making an illusion that tripped the satellite in orbit.
Both these stories show that a Nuclear Launch and impact has components that an alien ship would not necessarily display on radar and early warning launch detection that would be characteristic. Of course, the sudden destruction of London without any other impacts would not look like a nuclear exchange immediately enough that Moscow would reduced to a greasy black smudge on a map. Even, if some how, the radar and the satellites said it looked like a duck, the fact that London and only London was hit would prompt high tensions, but not an immediate all out war.
In military doctrine, especially related to Nuclear War, there are two types of targets: Counter-Force, and Counter-Value. London would be a Counter-Value target: A military target that, while not valuable to the war effort, is incredibly valuable for other reasons (like being a major world city). Though some of that value could translate to the war fighting effort, the sheer loss of wealth and life is the initial value in softening it for invasion. In Nuclear War, the real good targets are Counter-Force... aka other nuclear sights. This is why the U.S. is frequently seen with ground nukes in the center of the country instead of the coasts... because it's impossible for air plane nukes to get that far inland and it's easier to get them to launch without being destroyed by a first strike. This is also why Russian Nukes launched from ground are mobile... and why Submarines are so much valuable (they are both mobile and stealthy... they're almost always a Second Strike platform, as opposed to air and ground being First Strike exclusive. It's nice to blow up a city of 8-10 million people... but from the perspective of Nuclear War, the victory is blowing up an empty field with a multitude of nuclear silos under the ground.
Finally, the U.S. and U.S.S.R. maintain the "Red Line" which is an emergency communications channel from the Kremlin to the White House for the express purpose of figuring out what the hell without declaring a war. The mysterious explosion of London would prompt the yelling of both sides and insistence that they didn't do anything (it's not a real telephone, mind you... it's more of text base communication with translations so dictating, sending, translating and answering help to slow all of this down further).
With all of these factors, the governments, while confused about the sudden crash and destruction of London, would be hesitant to let the nukes off the chains for the time being... of course, the U.S. and U.S.S.R. would certain suspect the other was up to no good, but neither wants to die in a war for an action they didn't do and would insist on trying to work out the cause that gets them out of WWIII.