I've took some pictures while making this box and now I decided to show the process to those who are interested in it.
First of all I took small box from cheese (by the way cheese was yummy) and some denim scraps. Personally, I like to use those parts from jeans which have some wear on it which gives me different shades of blue.
Then I draw two circles. Simply put your choice of box on fabric and outline. Cut it out.
For this box I decided to make handle on top. I took belt loop and sew it in the center of piece which will cover the lid.
Now simply glue denim to the sides of box. I use craft glue. As you can see the length wasn’t enough so I measured another piece of denim and glued it.
This is the in-between result.
I incised the fabric not quite reaching the bottom. Put some glue on and fold fabric in the way you can see on pictures.
I happened to have some ribbon which perfectly matched the width of lid rim so I used it. If you don’t have anything like this just cut another piece of denim and glues it on rim. I recommend close the lid before gluing something on rim because there is the chance you may pull fabric too tight while gluing it and lid won’t fit.