I mean just read the link and they're objecting to a 120m-wide trench being dug through their countryside. Which is easy enough to sympathise with.
In this drawing, you can see the area in the map and it is not 120m wide along the trench: https://www.nationalgrid.com/document/357086/download. For scale, the grid squares are 1000m.
A 400kV trench construction swathe also includes the soil storage areas - subsoil and topsoil are separated for return afterwards, as well as clearance to the fencing (https://www.nationalgrid.com/document/357086/download).
(Re rail lines — if you build power lines over existing rail lines you could also electrify the rail route at the same time, and get rid of the diesel locomotives).
Roads also go to places with buildings and have junctions, plumbing, foundations and are generally hard to dig past. But there are places where they do follow motorways: https://commons.wikimedia.org/wiki/File:M6_motorway,_northbo... (also canals).
Rail lines go though towns by design, and as you see from comments even here, the one thing people really hate the thought of is power lines near houses.