[Grammar] No article with titles and positions

[englishhobby]

I know that in some cases we shouldn't use an article with titles and positions, like in Queen Elizabeth, President Lincoln. I also know that the article is not used in sentences like He was appointed president of the company in 2009. Are there any other cases when the article is not used with titles and positions?

 

[Tarheel]

David Cameron is Prime Minister of the UK.

 

[englishhobby]

Elizabeth II is Queen of the UK. Is it also correct?

 

[MikeNewYork]

Yes.

 

[Rover_KE]

Her name is spelt Elizabeth.