Shadow transport secretary Andy McDonald claimed there were missed opportunities to prevent the airport from coming under such an attack.
It comes as detectives continue to question a man and a woman over the chaos, which affected around 140,000 passengers this week.
Mr McDonald said: "The Government was repeatedly warned about the risks posed by drones to aviation but failed to act.
"The delay in bringing forward legislation is indicative of this government's failure to concentrate on the day-to-day business in front of them. They have taken their eye off the ball.
"The scale of disruption is unacceptable and it demands that we find out how this was allowed to happen, which is why Labour are calling for an independent inquiry."
On Saturday, the Times reported that Transport Secretary Chris Grayling had shelved plans to introduce legislation amid pressure on his department, with civil servants being diverted to prepare for Brexit.
But a Department for Transport spokesman said the claims were "a combination of nonsense and gross misrepresentation".
He added: "The drones at Gatwick have been flown illegally. The Government changed the law this year to make it illegal to fly drones within 1,000 meters of an airport or above 400 feet. The law couldn't be any more clear."
Sussex Police said the 47-year-old man and 54-year-old woman were arrested at about 10pm on Friday.
The pair are being held on suspicion of "disrupting services of civil aviation aerodrome to endanger or likely to endanger safety of operations or persons".
A house in Crawley - less than five miles away from the airport - was searched on Saturday, while Superintendent James Collis said investigations are ongoing.
"Our activities at the airport continue to build resilience to detect and mitigate further incursions from drones, by deploying a range of tactics," he said.
"We continue to urge the public, passengers and the wider community around Gatwick to be vigilant and support us by contacting us immediately if they believe they have any information that can help us in bringing those responsible to justice.
"The arrests we have made are a result of our determination to keep the public safe from harm. Every line of inquiry will remain open to us until we are confident that we have mitigated further threats to the safety of passengers."
Around 1,000 flights were cancelled or diverted after drones were spotted inside the perimeter of the UK's second biggest airport on Wednesday.
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