An investigation by the Marine Accident Investigation Branch (MAIB) found that Mr Milligan's wife, Victoria, was at the helm of 'Milly' but was not attached to the boat's kill cord - a safety device designed to cut power in an emergency.
The report said that when Mrs Milligan turned the boat to starboard to begin another run along the Camel Estuary, Mr Milligan, who was sat next to his wife, reached across and took control of the helm with his right hand and grasped the throttle with his left in order to execute a tighter, higher-powered turn.
As he did so, Mr and Mrs Milligan and their four children, who were holidaying in Cornwall from their home in Wandsworth, south-west London, were thrown from the speedboat into the water.
Because the kill cord was not attached, the engine did not cut out and the boat circled at high speed out of control hitting the Milligan family, who were all in the water.
Mr Milligan and his daughter Emily died, while Mrs Milligan, 39, and the couple's other children, Amber, 12, Olivia, 10, and Kit, four, were injured.
The runaway boat went on to inflict other injuries on water users until waterskiing instructor Charlie Toogood leapt from his own boat into the craft to turn off its engine and prevent further harm. He was subsequently declared a hero for his actions.
The MAIB report stated: "The turn to starboard which led to the ejection was initiated by Mrs Milligan but Mr Milligan almost immediately reached across his wife and took control of the helm with his right hand and grasped the throttle with his left.
"It is likely that he did this because he thought that a tighter turn to starboard was required to keep Milly clear of the beach on the Padstow side of the estuary.
"The manner in which Mr Milligan took the helm appears to have been out of character as he was known to be a safety-conscious and prudent individual.
"It cannot be established whether the wine he had consumed about one-and-a-half hours earlier adversely affected his judgment or fine motor skills when he reached across and took the controls, but his alcohol levels were well below the drink-drive limit for UK roads."
Immediately after the accident the MAIB issued a safety bulletin warning of the "culture" in which a "significant proportion" of drivers do not attach the kill cord when the take the helm.
In a statement, the Milligan family said: "We are still coming to terms with this tragic accident which has left us without Nick, a loving husband, father, son and brother, and Emily, whose life was only just beginning.
"We sincerely hope that awareness of this accident will mean that another family does not have to go through anything similar."
The report stated that on the day of the accident it was the first time Mr Milligan had taken the 300hp rigid inflatable boat out in 2013.
Mr Milligan had the kill cord attached to his leg during a series of runs at 30 knots between Gun Point and St Saviour's Point. Everyone on the boat was wearing lifejackets or buoyancy aids.
When the family stopped for a takeaway lunch at Padstow, Mr Milligan remained with the boat and drank some wine.
A post-mortem examination found he had 56 milligrams of alcohol per 100 millilitres of blood in his body at the time of his death. There are no regulations governing the drink-drive level for non-professional mariners.
Describing the accident, the report said: "Mr Milligan, who was in the co-driver position, suggested that they should turn to starboard for another run.
"Mrs Milligan was reluctant to do so as she did not consider there was sufficient space between the boat and the beach.
"However, due to encouragement from the children and Mr Milligan, she began a slow wide turn. Mr Milligan then reached across, in front of his wife, took the helm in his right hand and the throttle in his left, and then increased the engine throttle setting to full as he turned the helm to starboard.
"The boat immediately accelerated and heeled into the turn and then suddenly, and violently, rolled back to port and ejected all its occupants out over the port side and into the water. The boat then continued to circle under full power.
"The family were on the surface of the water, supported by their lifejackets and buoyancy aids, and the boat circled back towards them, striking several of them."
The report said the most likely explanation for the kill cord not being attached was that Mrs Milligan was expecting to take the boat back to its mooring at Rock and not do a further run.
"The use of a kill cord is fundamental to the safe operation of small planing craft," the report said.
"The evidence of this and previous accidents would indicate that kill cord use is still sporadic, and that much more needs to be done to make fitting a kill cord second nature when taking over the helm of a powerboat.
"The MAIB has issued a safety bulletin to this effect but more needs to be done."
The MAIB said it had made recommendations to the Royal Yachting Association (RYA) to review its powerboat training scheme to provide additional advice on the potential hazards posed by high-powered craft.
Mr and Mrs Milligan had both received a familiarisation handover when they bought the boat in April 2012 and also attended the RYA level 2 powerboat handling courses.
"However, this training and experience did not provide them with a good understanding of how their boat would perform in a high-powered turn," the report said.
"The speed with which Milly accelerated into the pre-accident turn, and the resultant hook, not only caught all six occupants by surprise, but it also came as a shock to Mrs Milligan that the boat was capable of such performance.
"Post-accident trials of Milly showed it to have some undesirable handling characteristics in certain circumstances, which could be mitigated by design changes."
MAIB chief inspector Steve Clinch said: "This was a tragic accident and I hope that the lessons resulting from the MAIB's investigation will be learned to prevent further loss of life in the future.
"Avoiding an accident by knowing your boat's and your own capabilities and limitations is essential, as is ensuring that all on board are safely and securely seated whenever manoeuvring or travelling at speed.
"I am pleased that the Royal Yachting Association has agreed to produce further guidance on both these subjects as part of its powerboat scheme.
"Should the unexpected occur and the boat driver be thrown from the helm or even overboard, having a device that immediately stops the engine can help prevent a serious injury or fatality.
"The kill cord is an essential item of safety equipment, and I most strongly urge all powerboat drivers to ensure one is fitted and correctly worn at all times when under way, and to regularly check that it is functioning correctly."
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