Eleven people are now feared to have died in the Shoreham disaster and the death toll may yet rise further, police said.
The CAA announced the following restrictions:
• "As a precaution, on Saturday 22 August we took steps to ensure no further flights were made by Hawker Hunter aircraft - this temporary restriction remains in place.
• "Flying displays over land by vintage jet aircraft will be significantly restricted until further notice. They will be limited to flypasts, which means ‘high energy’ aerobatics will not be permitted.
• "The CAA will conduct additional risk assessments on all forthcoming civil air displays to establish if additional measures should be introduced.
• "We commenced a full review of civil air display safety yesterday and held an initial meeting this morning."
A vintage Hawker Hunter jet plummeted on to the A27 after it failed to pull out of a loop manoeuvre during an aerial display, exploding in a huge fireball as it ploughed through cars on the busy road.
Pilot Andy Hill, an experienced aerobatic stunt flyer who performed at shows up and down the country and flies for British Airways, was pulled alive from the wreckage and is fighting for his life in hospital.
But police warned it is "highly likely" 11 people have died and warned the number of fatalities may increase as they continue to search the scene of the carnage.
Some 14 people were injured, four of whom were taken to hospital, after the jet crashed at about 1.20pm on Saturday shortly after beginning its display in front of thousands of spectators at the Shoreham Airshow.
Among the dead are Worthing United footballers Matthew Grimstone and Jacob Schilt, both 23, who were on their way to play in a match for the club, and personal trainer Matt Jones (24).
Mr Grimstone's family said they were in "total shock" at his death, adding: "He was the kindest person you could ever meet with, a great wit."
Another man believed to have died was the driver of a Daimler wedding car, who was on his way to pick up a bride for her wedding service.
Those caught up in the tragedy were remembered at church services this morning. Prayers for the crash victims and their families were said at St Mary de Haura Church, where a minute's silence was held.
Police are yet to formally identify any of those killed in the tragedy.
Sussex Police Assistant Chief Constable Steve Barry said: "This has been an enormously traumatic incident and our thoughts are with everyone who has been affected, from those who have suffered bereavement to those in the local community who are deeply shocked."
He added: "Sadly, as a result of our initial work at the site, which has continued overnight, and inquiries following calls to the emergency services from worried families and friends, we have now identified 11 people who we are treating as highly likely to have died in this tragedy."
Investigators are keeping "an open mind" about who has been involved in the crash as they continue to receive calls from worried friends and relatives.
He said: "The scene itself is incredibly large. A lot of specially-trained officers are sifting, as we speak, so we do need to keep an open mind, but from what we have seen at this stage it is possible that we will find more fatalities."
Removal of the bodies was carrying on yesterday and is likely to continue today.
Specialist recovery teams and air accident investigators have been scouring the scene searching for more victims and clues as to how the accident occurred.
The crash site is "extremely large", Mr Barry said, and is spread over 400 yards of the A27 and into the adjoining airfield. All of those who died are thought to have been on the road.
Investigators discovered earlier that there was still engine fuel aboard the plane and its wreckage will be removed by crane tomorrow.
Mr Barry said the status of the jet's ejector seats was yet to be determined but confirmed the pilot was pulled from the burning jet.
The A27 is expected to be closed for several days for the investigation to take place and wreckage to be removed. The road itself was also badly damaged and will need to be repaired.
Specialists from other police forces in the South East and the West Sussex Fire and Rescue Service have been drafted into help with the operation, which Mr Barry said was "very, very significant... the likes of which I have never seen before".
An Air Accidents Investigation Branch spokesman added: "A preliminary report will be published when the initial stages of the investigation are completed.
"We ask if any members of the public with footage or photos of the crash could provide them to the AAIB as they could assist the investigation. They can do this by contacting email@example.com."
Footage and pictures of the incident can also be sent to police, who urged people to contact them on firstname.lastname@example.org before sending any files.
As emergency services continued clearing the crash site, residents and loved ones came to the scene to pay their respects.
Dozens of bunches of flowers, yellow bouquets, roses and sunflowers lined the railings of a nearby footbridge.
One card read: "We didn't know you but we came because we care, we wanted you to know that you and your families are in our thoughts. Shoreham grieves for you and with you. Rest in peace."
Another said: "Thinking of all those who have lost their lives at the Shoreham air show on 22 August, 2015. Friends and family are in our thoughts. Rest in peace."
A message from St John Ambulance, Southwick Unit, read: "Our thoughts are with loved ones left behind."