This is important @Klogg because LPE customers are much lower users on average than the median customer. This means the network charge comprises a much higher proportion of total cost.
I know a few people in 2 person households who use LPE and have told me their cost on a repeat of their last 12 months electricity usage would have been between 11.4% to 13.5% lower had they been with LPE the last 12 months. With that said, network/supply charges would have made up as much as 33-40% of the bill (two person household), whereas my own family experience (5 or 6 person household) is that network charges comprise only about 14 or 15% of the tariff.
This is an LPE bill (network is 39.6% of tariff):
This is my own household bill (network is 14.6% of tariff):
You can also see why I'm so keen to see the contract my own household is currently on expire so I can switch to LPE, big savings to be had... - Eternalgrowth
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