"Your username or password is incorrect" except it isn't

I'm trying to set up icloud email on an android device. I have entered all of the imap info correctly. Howeve, I keep getting the message that my username or password is incorrect. I have tried dropping the @icloud.com as suggested. I have also tried it with @icloud.com and @me.com and @mac.com. Each time I get the incorrect username or password. I am absolutely using the correct password as well as username. What is wrong? I am a resident of the US with an iPhone, MacBook Air and iPad. However, I travel extensively to the UK and recently purchased a UK pay-as-you-go android phone. Can that have anything to do with it?