It reveals the figure is up 9.2% during the same period last year, when a record 5.8 million customers moved to a different supplier.
October saw more than 626,000 customers shop around and switch – down 1.1% on the same month in 2018.
Out of those switches, 32% were from larger to small and mid-tier companies, 29% between small and mid-tier suppliers, 23% between larger suppliers and 16% from small and mid-tier to larger firms.
Audrey Gallacher, Energy UK’s Director of Policy, said: “This month’s figures show that consumers continue to take advantage of the increased competition.
“With the temperatures dropping across the country, I’d encourage consumers to get in touch with their supplier or have a look online to make sure they’re on the best deal ahead of winter and the cold weather.
“More importantly I’d urge everyone to make their homes more energy efficient – for example by insulating the roof or installing LED light bulbs – as this is the best way to save money on your bills and at the same time do your bit to save the planet.”