It should be a permitted development right to electrify any existing railway right of way without requiring planning consent
Electrification and other works within the railway boundary are usually permitted development. This includes e.g. bridge reconstructions, as long as it's a like for like replacement.
Network Rail do engage with local planners, partly to set out why they believe it to be permitted development. Obviously may be different where there could be an impact on listed buildings or protected landscapes.
lines that are near power generation and substation sites where there is capacity to add transformers to tap into the primary grid should be easy wins
They do this where it's possible, particularly since (as I understand it), Network Rail will apply for a 25kV connection, meaning transformers are owned by others. So for the MML upgrade south of Bedford, National Grid put 400/25 kV transformers inside Sundon substation with a buried cable to take 25kV to the lineside.
Using modern technology rigid conductors can probably solve a lot of problems with tight bridge tolerances.
There are several examples of different approaches to tight clearances. Off the top of my head, the example that's most talked about is the bridge that carries the valley lines over the main line between Cardiff Central and Queen Street.
Edit: Just noticed it was your first post. Welcome, hope the above is of interest, searching the forum should turn up some links/previous discussion on the above.