Its not very direct, but it can be a good run if not too busy. From brum on the A38 head out through Lichfield, A515 through Yoxall, onto Sudbury, and to Ashborne. A515 towards Buxton, A5270 via Chelmorton, Millars Dale, Tideswell.
Bradwell, Bamford, (A6013), then A57 towards Sheffield, then A61 to Barnsley.
Hope this helps !