According to the Kent Police website, a report of disturbance was made at the Three Horseshoes pub on Main Road, Knockholt, on Friday 14 February.
Officers attended the scene with the South Coast Ambulance Service, where a woman in her 40s had reportedly suffered injuries that were consistent with gunshot wounds.
No ongoing risk
While the victim had not been formally identified, she has now been named locally as 43-year-old Lisa Smith, originally from Slough.
Smith was later declared deceased at the scene and a murder investigation is now under way.
Kent Police reported her next of kin have been informed and are continuing to search the River Thames because the person under suspicion of the shooting is thought to have fallen from the Queen Elizabeth II Bridge.
Kent Police senior investigating officer Detective Chief Inspector David Higham said: “Call handlers received reports of a man on the wrong side of the barrier and we are not ruling out the possibility that he may have entered the water.
“We are currently only looking for one suspect and do not believe there to be an ongoing risk to the public.
“Specialists officers continue to work with the families of both parties involved to support them following this tragic accident.”
A statement posted on the Three Horseshoes’ Facebook page expresses its “sincerest condolences to the victim’s family and friends”.
“We also want to send our support to anyone else in the local and surrounding community who has been impacted by this.”
Sensitive time
The post also urged people to “be respectful” during the current sensitive time period.
Knockholt parish councillor Steve Maines told the BBC: “We were sitting having our Valentine’s Day meal when, all of a sudden, we heard this commotion outside in the car park. We were told someone had been shot so we had to leave.”
Other individuals have also commented publicly on Facebook expressing their thoughts around the incident.
Sevenoaks and Swanley MP Laura Trott said she was “devastated to hear about the incident” and stressed she was aware the community is shocked at the news.
She added: “This is a live investigation and we must allow the police to do their job.”