Britain could have fallen to fascism but its politics, economy and geopolitical situation as well as the likely reprecussions of a defeat in WWI would be significantly different than Germany's so the results would be similarly different. My biggest gripe about Turtledove, especially that series, is that he almost directly transposes the history of one nation onto another. It's kind of amusing and entertaining, even thought provoking, but it doesn't make you feel convinced that you're reading a genuine alternate course of history.
Having said that I think I can give some ideas in the unlikely event that this did happen.
First of all, there will be strong emphasis on the uniqueness of England, its people etc. The racial attitude would be reminiscent of that held by Cecil Rhodes. Scapegoats for Britain's defeat would not be an ethnic minorty as in Germany but communists and socialists. The country would consider itself to be doing God's work and would employ increasingly hard-lined policies of assimilation and subjugation in the colonies. Military power would be a top priority and the country would build its strength up. As before, the British would emphasize provoking whatever enemy they wished to destroy into attacking them first rather than blatantly making the first move. They would go to much greater lengths to appear to the citizenry that the war was defensive and that the survival of the empire would be decided once and for all by the outcome of the struggle. Free speech would be stifled and justified as a necessary measure in wartime. Australia, Canada, New Zealand and South Africa would attempt to distance themselves or break away altogether during this time and would either be denounced as traitors or granted some serious concessions to keep them in the commonwealth. In order to stir up fear and force the loyalty of the dominions, the British will attempt to incite conflict with the Japanese, who are most likely to be seen as a threat against which Australia and New Zealand must rally. Germany is also portrayed as an enemy but with more caution since Britain, having spent a huge amount of money on things like enourmous capital ships, does not have the means to defeat them on land. The end result is an eventual coup led by a member of the royal family following alienation from other English-speaking colonies, economic and military disaster, and the loss of old colonies. I imagine Britain becomming isolated and Germany, eventually provoked or otherwise angered, beginning to devastate the country through submarine warfare and relentless aerial bombing. France and/or the USA may potentially intervene to prevent Germany from demanding unconditional surrender and, if Russia or the USSr is involved, the prevent their collapse too. Faced with an arrogant (if more liberal) Germany poised to achieve European hegemony and eliminate all counterballances, Britain could be seen as the lesser of two evils. The Americans might not be willing to commit much in the way of troops but they might well lend a hand in fighting the German subs and sending supplies to the British. Wow, this is getting weird, huh?