It's actually *relatively* possible. The late and dearly departed James G (I miss him every single day) wrote a bunch of conventional WW3 NATO vs Warsaw Pact alternate history. IIRC he had a second Battle of Britain occurring over London and makes reference to defensive preparations in case the Soviet Airborne tries a coupe de main in London.
Here's my idea (a preexisting framework I've long wanted to write but don't have the time to execute):
POD: Konstantin Chernenko slips and falls on February 5, 1984 and sustains a resulting aneurysm which kills him. Four days later Andropov dies.
-The USSR isn't quite ready for Gorbachev yet. Grigory Romanov, a hawk and close acolyte of Andropov, becomes General Secretary
-mid-1985: the USSR realizes that if they wait any longer they will permanently lose military advantage over NATO and will be stuffed in any subsequent conflict (this was the last year NATO and WP forces were really at parity before NATO pulled decisively ahead). Romanov, paranoid and famous in OTL for his bellicose rhetoric during Able Archer, decides to initiate a bolt from the blue war to take all land on the east side of the Rhine, Scandinavia, Southern Europe, and also to induce the DPRK to restart things on the Korean Peninsula (which Kim il-Sung wanted to do anyway; he was really lobbying the Soviets hard to try for Seoul again in 1975 after Saigon fell).
-Oleg Gordievsky, the KGB Ranking Officer in the UK and a secret MI-6 asset, is made aware that they will soon be at war (within two weeks) and is briefed on plans for the "Grey Terror" in the UK, the preparatory period in which Spetsnaz and agents from both the KGB and GRU would commit various acts of sabotage, disinformation, reconnaissance, and terrorism. He quickly alerts his handlers and provides copies of key documents and orders. His info includes information that naval spetsnaz will land by submarine on various locations in the UK a couple weeks before things start, along with landing locations. The Royal Navy is able to covertly observe and videotape Soviet submarines dropping armed spetsnaz in the UK from his info, incontestably proving that war will soon start. The information is quickly shared throughout all NATO, and general panic ensues. REFORGER, Britain's Transition to War plans, and all other national equivalents in every NATO country are activated.
-Two weeks later: war starts. Loss of strategic surprise results in the Soviets failing to reach the Rhine, though they do take Denmark and most of the FRG's territory. However, NATO loses all of Scandinavia, with Norway, Sweden, and Finland falling. Convoys across the Atlantic also suffer heavy losses, though an airborne drop into Iceland is defeated. The Soviets are helped greatly here by the fact that all U.S. Navy encrypted comms (which are also used by the USMC, which has the main responsibility for the defense of Iceland and Norway) are being intercepted and decrypted in real time due to the espionage of the Walker Ring. This is the state of things one month in.
-With the Skagerrak and Norway securely in Soviet hands, they are able to send the Baltic and North Sea fleets through to meet each other. They consolidate at Bergen. The Soviets now have a much more potent surface fleet than the Nazis had, with the Brits and NATO having much weaker in comparison to their forces in WWII. Attrition in the North Atlantic and everywhere else, coupled with prewar sabotage of the Panama and Suez canals, means NATO can't put many ships in their way as a permanent defense. Britain and the rest of NATO have had to commit virtually all of their armed forces to Germany and the Low Countries to keep them from falling. As this is only a month in, there has not been time to truly stand up a draft and increase the size of the military; recalled veterans and new enlistments have to be used as casualty replacements. Troops in the actual UK consist of some Royal Marines who escaped Norway and a couple reserve brigades. In OTL for the record, the British army of this period consisted of four divisions and a few reserve brigades, and all four divisions were designated for NORTHAG. So IMHO that's realistic.
-The Soviets realize they're snaked in Germany. NATO's defense there is unbreakable. They notice, however, the British defenses are relatively weak. They launch a surprise landing of airborne units in Essex, backed by naval infantry and leg/armoured units carried by the combined Soviet fleets at Bergen. The goal is to either draw units away from Germany and possibly allow a breakthrough, force Britain to withdraw from the conflict, or sue for peace from , a position of relative strength and try to get status quo antebellum plus maybe some minor concessions. They gain a hold but weak logistics and heavy urban fighting on the outskirts of London grind them down. The Brits are few, but they are on their home turf and their logistics are much easier, and they are better trained and equipped. A flood of Irish (who threw in with NATO at the beginning), Iberian, and American units stabilize the front. Submarines attrit the Soviets' supply lines and ultimately the Soviets are pushed off the isles. The gambit is unsuccessful.
-NATO wins at some point, taking East Germany and the Czech half of Czechoslovakia as well.
That's my idea.