Hi. I think you would be absolutely fine to just make your beds where you want them on top of the existing grass. You could put a cardboard layer first, wet it well then put the compost on top. I think Charles would say that if you have 4-6 inches of compost to go on top you may not even need cardboard, as the compost will block the light completely from the grass.
If you look at the videos on this site you’ll get a lot more detail, but the good news is that you dont need to till it first. I have done this and am already planting into the compost – bare root plants such as black currants, and some raspberries I had in pots seem to be loving it!