Well for short distances, like a low bridge or a tunnel, or Wigston-Syston, then you could just run an insulated +25kV/0/-25kV cable in the cess to provide electrical continuity.
For longer gaps, sure, you would need a grid feeder for electrified islands. But not that many: at 90mph this train would have a range on battery only of 8 minutes, but running the diesel engine as a range extender would give you 20 minutes, which is 30 miles. This is the distance from Yate to Gloucester or from Cheltenham to Bromsgrove. So you would only have to electrify Cheltenham to the Gloucester triangle to decarbonise the whole of Bristol-Birmingham.
And I note that Tamworth is 15 miles from Birmingham, and 25 miles from Derby. Tamworth high-level could be supplied from the WCML without needing a new grid feeder at all. You could electrify / batterify the whole cross-country route from Bristol to Edinburgh with just one new grid feeder at Cheltenham.