I think it would take more than one divergence, but let's see what I can do. This is a bit Rube-Goldberg, so bear with me.
Step One: Winter 1939/40 gets serious about three weeks early and ends three weeks to a month early.
Implications:
(a)The Soviets postpone the Winter War with Finland rather than send unprepared troops into ongoing blizzards. The Soviet attack is postponed until spring.
(b) The Allies don't have the "help Finland" excuse to intervene in Norway and proceed with contingency plans at a much slower rate.
(c) Mussolini doesn't grandstand by sending weapons to Finland as he did historically--which historically was a bad move because the Soviets cut off sales of their oil to the Italian navy, leaving it with precariously low supplies.
(d) With no imminent Allied threat to Norway, Hitler figures Norway can wait until France falls.
(e) Without the disastrous Allied response in Norway, Chamberlain hangs on as British Prime Minister through the Battle of France
(f) The Battle of France starts around April 10-15, as soon as the mud dries enough and the sky clears. The Germans were ready and champing at the bit by that time and the French had adopted the Breda variation of their Dyle plan, which disastrously sent the bulk of their mobile reserves about as far from the crucial part of the battle as they could have been. The crucial variable that historically postponed the German attack was the late spring and persistent mud.
(g) Without the Norway attacks, German use of airborne troops in Holland is more of a tactical surprise, something that had been theorized about rather than something the Germans had actually used already. As a result, the German airborne attacks are more successful/less costly, succeeding in the attempted decapitating strike on the Dutch government and cutting airborne and transport plane losses.
Step two: The Battle of France happens about the way it did historically, but about a month earlier.
Something similar to the Dunkirk evacuation probably happens, but with less success. Historically the Brits got lucky in that several crucial days were rainy, keeping the Luftwaffe at bay and allowing the Brits to load during the day for several crucial days, but the channel was calm. That's a very unusual combination. No rain would mean that the evacuation would be restricted to the eight hours of night, as it was historically on clear days. Historically, that cut the guys evacuated to about one-third the rate they managed during the rainy patch (8 hours versus 24 hrs). There are other variables, such as the evacuation possibly lasting longer, but as an approximation the Brits get out one-third of the guys they did historically. They might not be as generous in getting French troops out in that situation, but allied unity would require that some French troops get evacuated. So the Brits get somewhere between one-third and one-half the troops out that they did historically.
So it's late May. France has surrendered.
(a) The Brits have considerably fewer of their best-trained troops available.
(b) The German navy hasn't been virtually destroyed in the Norway invasion as it was historically.
(c) The German airborne forces are in considerably better shape, both because they did better in Holland and because they didn't lose the 300-odd transport planes that they historically had to write off in Norway.
(d) The Brits still have Chamberlain as prime minister, at least for a time. I doubt that he would have been displaced during the Battle of France. He would be vulnerable once it ended.
(e) The Brits would have had a month less to outproduce the Germans in fighter planes and train more pilots
(f) Historically, the Brits just had to survive until early October, when weather in the channel made an invasion essentially impossible. The earlier fall of France means the Germans have an extra month when the Brits are vulnerable.
(g) (From old and possibly faulty memory) The Brits were historically temporarily cut off from ultra intercepts by some German code changes, but got their capability back in time to realize in early July that the Germans were nowhere near ready to invade and there was no immediate need to negotiate.
At that point, it's all a matter of how leaders perceive the situation and react. Sea Lion is probably still not possible, but the Brits situation is dependent on perceptions. The Brits themselves have to perceive, after the shock of defeat in France, that the Germans aren't ten feet tall. The US has to perceive that Britain will fight and can survive. Otherwise they'll hoard military equipment instead of sending it to the Brits. No fifty destroyers. No 500,000 small arms sent to Britain. Probably fewer planes. Japan has to be sufficiently deterred to not go after the Far East colonies. If Japan realizes how weak Britain is at this point, they can grab 90-95% of the world's rubber supply and humiliate Britain, possibly loosening the Brit hold on India, which historically became precarious after the Brit defeat at Singapore. Spain has to be deterred from letting German planes on bases within easy range of Gibraltar.
Under this scenario, I would still say the Brits have a 60% chance of avoiding defeat, but if they lose their nerve a whole lot of bad tumbles down on them, with a lot of other jackals joining Mussolini to try to grab a piece of what they perceive as a dying lion.
