I was lucky to find one of the books mentioned on the Basketry Taster course in our local library and I would certainly recommend it. Even if you have no interest in learning any of the suggested techniques it is an interesting read and it largely suggests working with readily available and often recycled materials. There are some lovely professional examples in the gallery section.
I probably will not take it much further but it has introduced me to new ideas and on a recent walk in the countryside I was looking for possible materials and testing them out, coiling them round my wrist, my companion thought this a bit odd. So the book is 'Practical Basketry' by Stella Harding and Shane Waltener.
I tried twining using a plastic cup and then went for something slightly bigger, did you guess:-