I've just started quilting and find a lot of things can be confusing if your starting in the UK and reading posts from the US!
I am doing my first block swap with the US and the instructions said to use unbleached muslin for part of the block - which was a bit daunting as muslin to me is very thin and certainly wouldn't be something I used out of choice - then I did a little research and come up with some translations of the differences between US and UK terminology.
Muslin(US) = Calico(UK)
Calico(US) = Printed Cotton(UK)
Cheese cloth(US) = Muslin(UK)
Back to the question - I agree you can get some great all cotton sheets that look to be about the right weight - I have seen some in Asda in UK - which is owned by Walmart so maybe you also have them in US?