I have successfully used the kind of permeable membrane you get in garden centres for suppressing weeds. OK, it's not, by definition, waterproof but it is light and is strong enough to be helpful under a thin tent floor. I've also found it a useful material for the porch or other rained-upon areas around the tent because it lets most of the water through and doesn't form puddles.
When The Helm tent was mentioned I thought, shall I look at this tent seriously again? I looked and gave up its a 2 person tent! On the Naturehike site is their Taga 1 the nearest model?
I use a piece of tyvek under my tent where I sleep, it weighs about 100 grams. Have a look on ebay there was someone selling person size pieces for just under £5. Waterproof, tough, light, and cheap so it doesn't matter if it goes missing.
I've heard of Tyvek being used before - is it not a bit crackly? Or am I mistaking it for something else?
Enjoyed your photos from south lakes, I might have seen my house in the panoramas of the bay, ha!