To make a Paddington the Bear hat, cut a tube, an oval shape and a wide rim piece from red felt, and sew them together. Invert the hat so the seams are inside before tying a length of rope around the rim.
Begin by cutting a large circle of red fleece that is wider than the teddy bear's or child's head, and cut a large hole in the center that matches the approximate dimensions of the head to create the brim. Measure the inside of the circle to find the length of the rectangular piece for making the tube. The tube should be approximately 3 inches tall for a small teddy bear. After sewing the tube together, pin it to the brim of the hat with the wrong sides out, and sew these two pieces together.
Cut an oval piece that matches the dimensions of the tube, and sew it to the end of the tube opposite the brim. Invert the entire hat, adding some elastic strips on the inside to attach to the teddy bear's ears, if desired. Fit the hat on the bear's head before tying a length of thin rope or twine just above the brim. Push in the top and sides of the hat to give it a creased appearance.