Hi, and welcome to the forums.
I don't know how well you get on with your coach so it's hard to say if you should ask. I would normally say 'No'.
The SkateUK program has certain elements to be completed - you should have a log book with these moves listed and the ones you've already done signed off. What has happened so far for you to get to level 6?
Around level 4/5 Kayleigh started having 15min private lessons which did advance her a little quicker. She still had her group lessons but on one or two occasions she went up a grade or two within the 6 week course/level period.
It may just be an idea to ask your coach what your weak points are for the grade you're on, and for any tips to help pass them. That way you've expressed an interest in wanting to move on to the next level without actually asking, if you see what I mean.
Good luck,
Steve