Once I had cut out all the pattern pieces in silk and wool for the lining, I sewed the thumb pieces to both the silk and then did the same for the wool. After this I placed a wool piece and a silk piece together with right sides facing and sewed around the edge (leaving the bottom part free) with a 1/2" seam allowance.
Having come to a problem of the mitts not fitting I stopped sewing them until yesterday. When I pinned along the seam line I found that they did fit and that they were a little bit tight around the wrist area when I tried to put my hand through, I resolved this by sewing a another seam a couple of millimetres closer to the edge of the fabric along the wrist area on one side.
Once this was done, I turned the mitts the right way round and ironed the seams flat (placing a handkerchief between the wool and iron to protect it). I then sewed up the bottom seam of the mitts and then the thumb piece at the top - this was quite fiddly as it's a small hole so some patience is required!
After that, it was time to sew up the main seam. I used a ladder stitch for this and doubled up the thread for extra strength. I sewed the lining seam and then the silk seam, but either way would be fine.