Hi, well done for persevering despite the lumps!! I cannot abide them and would rather go hungry!!
What works for me is a proper blender (with jug and base etc) and i add 250 mls water, the sachet and give it a quick whizz, then add almost an entire tray of ice and whizz for about a min. It is noisy as hell, but when it goes quiet you know its done! That will then give me about a pint of thick icy shake a bit like a cross between a slush puppy and a McDonalds milkshake ( sort of ;-) ) and it lasts for ages.
If you don't have a blender and intend to do Cambridge for a while I would def invest in one, or beg, borrow or steal!!!
Hope that helps,
happy blending!!!
Katy x