Police have now confirmed two adults and two children, all from Tealby, were in the car which left the B1203 Rasen Road and hit a pole carrying electricity cables this morning (Monday,September 1).
The driver, a 29-year-old woman, and the front seat passenger, a male aged 36, both received burns when they got out of the car, a beige Citroen Xsara Picasso.
The two back seat passengers, both boys, aged six and eight years-old, were uninjured.
The two adults were taken to Grimsby Hospital, where they were admitted for treatment and further tests.
More than 180 homes and businesses were left without electricity following the incident at 9.43am.
A number of supplies have now been restored, with the rest expected to be completed by 7.30pm this evening.