"No more", "no longer", "not anymore"

• "You don't love me anymore" is the most natural and common way to say this.
• "You no longer love me" is grammatically fine, but sounds a bit formal and stiff. It might be used in writing, but probably not in speech.
• "You love me no more" sounds very old-fashioned. You'll find sentences like this in classic literature--especially poetry--but not often in conversation.

That's why the English guy laughed. What you said wasn't wrong; it just seems very old-fashioned and stuffy, when it sounds like the effect you were going for was forceful and angry (I'm assuming you said "I use your service no more" because of some sort of problem with the service you had received). There may also have been a discrepancy between your tone of voice and the way the English guy perceived your words, which he found funny.