The cost of electricity has surged to record highs across Europe, following a meteoric rise in natural gas prices that could pave the way for painfully high consumer rates across the continent through the winter and well beyond.

Electricity futures across much of the continent jumped above 600 euros/MWh last week, an exponential gain from the roughly 20-30 euros/MWh average over the last decade. In a note on Wednesday, Rystad Energy analysts wrote that records have been broken on an hourly and daily basis throughout the month. 

“Should the current trend continue, then winter power prices will be punishing for European consumers large and small,” said Rystad analyst Fabian Rønningen. German and French power prices hit fresh highs as the week came to an end. French...