The owners of two properties in Rushock and Cakebole discovered they had no power when they woke on Monday, September 10.
After a closer inspection the owners discovered part of overhead power cables had been stolen, cutting off power to their homes.
A clock at one of the properties stopped at 2am, so the theft is thought to have happened then.
Thieves appear to have gone prepared as markings on the wooden poles suggest they were wearing specialist climbing shoes or spikes.
They stole about 600 to 700 metres of 240-volt power cables in total, worth about £2,500.
Police are now asking residents, who live near to power lines, to be on the look out and report any suspicious activity.
A representative from Western Power Distribution (WPD) said: "Metal theft is a nationwide problem but it has escalated in the last few years and is currently costing WPD around £1.5 million a year to put right.
"It affects our substations, but even overhead and underground lines have become targets, which is hard to believe when you consider the extremely high voltages involved.
"It's also incredibly inconvenient for our customers, especially those in rural locations who find that their power supply is disrupted.
"We're stepping up our security, and working closely with the police at a local and national level.
"If anyone discovers any cut power cables they should not touch them and call their power company or the police as soon as possible, so it can be made safe."
Anyone with information about the cable theft is asked to call police on the non-emergency number 101, quoting incident 242-S-100912, or ring Crimestoppers anonymously on 0800 555 111.
If you believe a crime is in progress, police say to always call 999.