They also do not acknowledge the Church of England yet it is still considered "Christian"
Not true. The Vatican does acknowledge the Anglican church, and had dialogues with it in the 80s (I think) to bring the 2 churches closer together. I don't think much has come of it, though.
Having said that, I agree that the RC church has been presumptuous over the years in regarding itself as the one true church.
On Mormons: conservative/evangelical/fundamentalist Christians would say that what matters is what do you believe about Jesus himself. Mormons, I understand, don't believe Jesus was God Himself, come to earth. They have added another "sacred" book on top of the bible, where the bible itself says it is complete and is not to be added to or taken away from (see the last few verses of Revelation). I think if you looked at the Book of Mormon, which Joseph Smith claimed to have found on inscribed plates in the US in the 1800s, it reads like someone tried to make up a new bible, using English that tries to sound like the King James version of the Bible.
The Jehovah's Witnesses are similarly a sect (or cult) that came out of Christianity in the US in the 1800s, but don't believe in Jesus as God. Also, a key principle of Christianity, at least to Protestants is "by grace you have been saved, through faith: and that not of yourselves, it is the gift of God; not as a result of works, that no one should boast..."(Ephesians 2:8,9). That is, you can't work your way to Heaven, it is a gift from God that comes from having faith in Him. Mormons, JW's and others try to work their way to heaven.
So Mormons and JW's and some other sects are not considered Christian because they differ on some fundamental things. Whereas different Protestant Christian denominations - Baptists, Methodists, Anglicans, etc. differ on forms of worship and finer points of Bible interpretation, but not on fundamental beliefs.