Do I have to keep a mental image of the keyboard and my hand placement all time as I suspect?
Yes, you need to know where your hands are but more importantly for grade 2, you must learn to read the intervals, so you do not have to remember which finger to use. You need to quickly recognize the difference between lines and spaces where you could play a third up or down, a second up or down, etc from anywhere without thinking about positions of your hand to the keyboard, just from where your last note is.
Also, do learn your scales well. They really help sightreading particularly learn G major and F major related minor scales. Before you begin playing, always ask yourself "what is the key signature?" They will help you not forget to play the F# or Bb if you know your scales and remember to check for key signature. I do not believe you will see keys with 2 sharps or flats for grade 2 reading exam.
Before you begin play during the exam, remember to check time signature, key signature, scan the music for accidentals, then play and count, out loud if you have to. Remember to breath deeply and relax. You'll do fine.