It turns out most people don't really care about a power line, but do like money. You won't have to offer much money to have a majority saying yes.
NIMBYism is 99% wealthier people pushing the costs (visually or literally) of modern society onto others instead of bearing it themselves.
https://www.politico.eu/article/uk-government-electricity-py...
It's currently "we'll give you £250 off your bill per year, for 10 years, if you let us build the pylons near you" (the average bill is currently £880 per year)
https://www.gov.uk/government/news/households-near-new-pylon...
Localized ballot initiatives are basically unheard of in the UK, though. Everything is routed through central government and its press officers.
Last I was comparing houses in a neighborhood, the houses near a powerline were consistently worth 15k-30k less (3-6% less).
Being given money immediately for your living costs might be more attractive to you, than trying to retain value in an asset you'll only realise in 20 years time when you sell it, or perhaps not at all if you die first.