Britain going Fascist is possible , forget Hitler through, it will not go Nazi.
So if after WW1 the social situation is worse with veterans feeling cheated, popular discontent rises, Mussolini's march on Rome is emulated but more in the sense of a bigger and earlier Jarrow March. Labour and the Unions stay quiet and refuse to back it similar to OTL meaning veteran/working class support starts moving to the Fascists.
Sometime in the mid-late 20's the BUF ( for want of a better name ) becomes a major force in British politics. The depression hits and it wins the election via the popular vote ( the existing parties are blamed, Labour especially being punished/broken for not supporting the working man/veteran during the march ).
Now given the nature of Britain its not going to be as anti-Semitic as the other Fascist parties, more them and us with us defined as the empire, so anti-French/American/Russian due to perceived actions in WW1 leading to Britian's issues.
Fast forward to the rise of Hitler, initially supported by the BUF but getting much colder as his polices become clear. Munich still goes as OTL since no butterflies for Britain trying to avoid another war but the British military is in a better shape due to military spending being used as a stimulus to try and get out of the depression. Since shipyards would be otherwise idle and planes were sexy, the bulk of the extra spending is on ships and planes ( Second London Naval treaty does not happen due to more mistrust so more refits followed by ships starting to be laid down in 1936, KGV's being 45000 tons, carriers larger etc. Planes will be more numerous and may be different but the thinking of the bomber always getting through will still cloud things ).
Poland is still the flashpoint, Britain even under a fascist government is not going to let Germany expand that much so you end up with a alliance of necessity between Britain and France. Less trust will mean the UK's contribution in France may be lower on the ground but a stronger air component and more naval activity. The British commanders will definitely have orders to keep their lines of retreat to the sea open.
Norway, goes better for the Allies, more patrol planes and submarines mean its seen as an invasion not a break out and the RN gets in place. Oslo airport still falls to a paratroop attack but the seaborne invasions are destroyed or turned back. Vicious fighting takes place but the inability of the Germans to take a port means the invasion is a costly failure.
As the French are still as badly organized as OTL France still falls, however the BEF gets back in better shape and, due to more spending and hence more escorts, the Battle of the Atlantic is much more in Britain's favor ( obviously Norway being allied helps a lot but politics means its trumpeted as a RN victory ).
Italy dithered due to the German defeat in Norway and does not declare war in time, they ask Hitler for spoils in return for joining after France falls but flush with victory he turns them down. Britain he declares will seek terms now. Britain as per OTL vows to fight on and the Battle of Britain goes more or less OTL just less panic on the British side due to larger reserves. Hitler asks Italy to join but Mussolini by now is in a huff and rebuffs him.
A standoff then ensures till Hitler decides to invade Russia .....