UK Power Networks own and maintain the electricity lines and cables that power over eight million homes and businesses in London, the East and South East of England. This means that the electricity is kept on regardless of who you pay your electricity bills to.
So if your electricity goes off due to a supply fault, you contact UK Power Networks:

Telephone:    0800 31 63 105
Mobile:          0333 32 32 105
Mobile text:  Text POWER plus your POSTCODE to 80876
Website:        ukpowernetworks.co.uk