Peak Rail actually are in an interesting position.
1. They have the lease of the track bed from Rowsley South to Matlock, in the original agreement with the District Council they had to create a concessionary footpath from Matlock to Rowsly Soutn
2, They own the bridge over the River Derwent at Rowsley (behind the Peacock Hotel)
Peak Rail do want to extend to Buxton, realistically to do this would cost in the region of £110m (2004 costs based on the DCC feasibility study), the PDNPA have indicted that there should be no rail termini in the National park, so that in theory rules out just running to Bakewell. I believe that the track bed is protected in case that it is re-opened and integrated into the national network