Electricity theft - which can be carried out by tampering with a line or bypassing a meter - has the potential to cause serious injury and is punishable by up to five years in prison.
Though already an increasing problem, the National Energy Action campaign group said it is "horrifying" that others could be turning to the illegal practice to keep their lights on amid a growing fuel crisis.
Home Office figures show West Yorkshire Police received 424 reports of the "dishonest use of electricity" in the year to March – up from 388 in 2020-21, and the most since comparable records began in 2012-13.
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Across England and Wales, 3,600 such offences were recorded in 2021-22 – up 13% on the year before and the most since comparable records began in 2012-13.
Around 1,100 of these occurred between January and March – almost double the number recorded over the same period in 2018-19 and 2019-20.
Stay Energy Safe, operated by Crimestoppers, says tampering with a meter can lead to wires overheating, the damage of property and potentially loss of life.
It also warns that the crime costs energy companies a minimum of £440 million each year – with these costs then passed on to customers.
An Ofgem spokesperson added that “under no circumstances should consumers attempt to connect electricity meters themselves”.
But the NEA said the cost-of-living crisis is forcing people into "increasingly desperate situations" such as avoiding energy use – including using candles instead of lights – or possibly even resorting to electricity theft.
Peter Smith, NEA director of policy and advocacy, said: "This is not only illegal but dangerous too, and it’s horrifying if the crisis is forcing households to try this to keep the lights on.
"And this is happening now, before winter and the cold weather hits."
When former Chancellor Rishi Sunak announced a cost-of-living support package in May, the NEA said the predicted average annual energy bill from October could hit £2,800 – but this in now expected to reach £3,358.
Mr Smith added: "More support is desperately needed to close this gap and help the most vulnerable keep themselves warm and safe this winter.”
Across all police forces, 57% of dishonest use of electricity cases were closed last year with no suspect identified.
In West Yorkshire, 405 investigations were concluded in 2021-22, with 47% resulting in no suspect being identified, 40% abandoned due to evidential difficulties and 8% with a charge or summons.
The Government said it is providing £37 billion to help households with the cost of living.
A spokesman added: “We are committed to cracking down on crime, including the criminal theft of electricity, which causes serious injury to people and damage to property."