It's amazing how much lawn clippings you can cram into your green waste wheelie bin.
I usually put a layer of branch cuttings at the bottom to ensure it will empty properly when the garbage truck arrives.
And never let water get in when you do the following or else you will be lucky if half the content empties out on collection day.
Every two catcher loads I get on a milk crate and step in the bin and push it down with my feet and it really frees up a lot of space each time. Where practical, I will put branch cuttings or other green waste between the layers and the grass will be forced into the spaces amongst the other waste.
As long as no rain gets inside, it will empty fine each time after all the packing.
You can even ask a neighbour close to collection day is they mind you pouring a load or two into theirs as people often don't fully utilise their green waste bins.