To play a piece of music you have never seen before takes a great deal of skill. So how is it, some musicians can do this easily such as session musicians and others such as non professional players of all standards find sight reading so difficult.
Don't confuse learning to play a piece with sight-reading a piece
Many players confuse learning and playing a piece of music with sight-reading. You also have to learn how to sight read and this is completely different from learning to play a piece of music. To sight read successfully does not necessarily mean playing the piece note for note but to get through the piece from start to finish, in time, that means no slow downs or speed ups, perfect time.
Stopping and starting
As a professional musician you do not have the luxury of stopping and starting as many non professional players do, and there are a great deal of very good amateur players that keep stopping and starting because they don't have the discipline of a good sight reader.
Learn to sight-read
The best way to learn how to sight read is to find a piece of music you have never seen before, start playing at the beginning and don't stop, until to reach the end. Yes, there will be mistakes and that is part of the learning process. You are learning to sight-read. It is a discipline that professionals are forced to use and unfortunately, amateurs just don't get. They have to play everything perfectly, which means lots of practice on just one piece of music.
The more music you sight read the better you will understand music phrases you have never seen before, the more music phrases you play the better you will get, the better you get the easier the sight reading becomes. It's a vicious circle, it's a great discipline and it will force you to use all of your music knowledge.