The F Major scale can be tricky to begin with as the right hand fingering starts with thumb under the 4th, instead of the 3rd, which is different to most other scales that start on a white note. I would suggest lots of hands separate practice to begin with (1 and 2 octaves) followed by hands together very slowly when you think you’re ready. In the earlier ABRSM piano grades you will be required to to play the scale 1 and 2 octaves hands together and in later grades you’ll be expected to play it up to 4 octaves hands together or contrary motion (2 octaves starting with both thumbs on F). To increase the number of octaves in the scale scale all you need to do is simply put the thumb under again in the right hand and 4th in the left hand and repeat the fingering pattern again. Also note that your right hand should be on finger 4 when you reach the top of the scale. The left hand hand fingering is the same as the C Major scale. It may be helpful to follow the notes along using a scale book as a guide. You can obtain ABRSM piano scale books from most local music shops in Swindon as well as online.  

Here is the piano fingering for the F Major scale as taught in my lessons:

One octave R.H (up) 12341234 (down) 3214321

One octave L.H (up) 54321321 (down) 2312345

Two octaves R.H (up) 123412312341234 (down) 32143213214321

Two octaves L.H (up) 543213214321321 (down) 23123412312345

Watch video demonstration of the teacher playing the F major scale: