Police warned this morning that the death toll could rise to 20 after a Hawker Hunter jet crashed on to the A27 during an aerial display on Saturday.
The BADA issued a statement on Sunday that expressed condolences to the family and friends of those affected by the accident and that sought to reassure the public over public safety around aerial displays.
The statement said the UK had an "exemplary" record for public safety at air displays and that the last time a member of the public had been killed at one was in 1952.
The statement added: "This record reflects the maturity of the multiple checks and balances that UK aviation regulators and airshow practitioners have developed."
The BADA said the UK had "extensive rules" covering safety and was "the envy" of other nations in this regard.
However, this has not prevented questions being raised over the safety of air shows, and the Civil Aviation Authority said last night that it was considering whether safety requirements should change.
However, the statement said that the BADA "will not speculate on how or why this particular accident occurred", going on to say: "Some people might find that frustrating but at this stage even ‘informed’ speculation, without full knowledge of the facts, is unhelpful."
Sussex Police has kept the public informed about its investigations via Twitter, and has appealed to the public for anyone with information or footage to come forward. However, it also warned members of the public to "think twice" before sharing images or footage online out of respect for those affected.
Have footage or info re #Shoreham aircraft crash? Email contact details to email@example.com and we'll be in touch.— Sussex Police (@sussex_police) August 22, 2015