The 787 was grounded by the FAA from January to April after a series of battery failures that resulted in at least one electrical fire.
The Dreamliner airplane that caught on fire last Friday was being operated by Ethiopian Airlines.
Britain's AAIB said it was confident the London Dreamliner fire was not related to the 787's batteries.
"There has been extensive heat damage in the upper portion of the rear fuselage, a complex part of the aircraft, and the initial investigation is likely to take several days," the agency said in a statement. "However, it is clear that this heat damage is remote from the area in which the aircraft main and APU [Auxiliary Power Unit] batteries are located, and, at this stage, there is no evidence of a direct causal relationship."
The 787 has had a turbulent introduction since its rollout last year. Prior to its grounding, the Dreamliner was touted as a revolutionary airplane, in part because of its use of lithium-ion batteries to reduce energy consumption during flights.
Boeing has maintained that the 787 has always been safe to fly. The company issued a fix for its battery issues that was approved by the FAA in April.