Perhaps because there was never really a need for such a radical regime like fascism in the U.K. We see in Germany - under the Weimar Republic - mass amounts of hyperinflation, different governments on a yearly basis, political and social standoffs. Germany was really going through a crisis of identity too, especially after the war. So fascism would have been an attractive political ideology for many Germans in desperate need of a better life. (Apologies I'm not too knowledgeable about Spain and Italy)

In comparison Britain were doing relatively well compared to some of their European neighbours. They were thriving economically during the roaring 20s and were reaping the rewards after WWI. Furthermore, especially after the Olympia Rally in 1934, the BUF were generally seen as violent thugs, attacking anti-fascists and Jewish people on the streets of London - which tremendously halted their support and isolated their following. The British press also played an important role, as, most notably the Daily Mail and Lord Rothermere, withdrew open support for the BUF, causing the public opinion regarding Oswald Mosley to decline and turn sour. The U.K. Government also banned the 'blackshirts' political uniforms and effectively made it harder to protest for the BUF (Public Order Act 1936).

It seemed people never really took the BUF seriously, they were viewed as a thuggish cult run by an eccentric Mosley. The Guardian writes "Mosley’s hope that political disorder would eventually precipitate a crisis that would sweep him into power." But this political crisis never happened, and as WWII broke out the public just sort of..forgot about him..

Just a thought. Again, apologies for not knowing much about Spain or Italy, hopefully someone else can help you on that front!