Friday is likely to be the busiest day of the year, with air traffic controllers expecting to handle more than 8,800 flights - a record number.
They have called for a drastic modernisation in the way aircraft are guided across UK airspace.
It comes as the government launches a discussion to shape the UK's aviation industry for the next 30 years.
Air traffic controllers expect to manage a record 770,000 flights in UK airspace over the summer - 40,000 more than last year.
But the ability of the the UK's National Air Traffic Control Service (Nats) to deal with this surge is being stretched to the limit, it is claimed.
Nats director Jamie Hutchison said: "In the last few weeks we have already safely managed record-breaking daily traffic levels, but the ageing design of UK airspace means we will soon reach the limits of what can be managed without delays rising significantly."
The Department for Transport estimates that, if airspace management remains unchanged, there will be 3,100 days' worth of flight delays by 2030 - that is 50 times the amount seen in 2015 - along with 8,000 flight cancellations a year.
The government wants the public to submit ideas on a wide range of subjects, from airport bag check-ins in town centres to noise reduction targets.
The six themes it will consult on over the coming months are:
Transport Secretary Chris Grayling said: "Our new aviation strategy will look beyond the new runway at Heathrow and sets out a comprehensive long-term plan for UK aviation.
"It will support jobs and economic growth across the whole of the UK.
"Our vision puts the passenger at the heart of what we do, but also recognises the need to address the impacts of aviation on communities and the environment."
Meanwhile, airport capacity is expanding way beyond Heathrow's new runway.
Friday also marks the start of a Â£1bn investment programme to double the size of Manchester Airport's Terminal 2.
The number of planes taking off and landing at Stansted has gone up every month for almost four years.
Cardiff Airport has seen an 11% rise in traffic, and Luton is recording growth of 7% this year alone.
The problem of volume has been complicated by shifts in travel patterns.
Destinations including Egypt, Turkey and Tunisia have lost out to Spain, Italy and the US, which means major changes in the flows of traffic into UK airspace.
Nats itself is rolling out a new Â£600m ($747m) computer system known as iTec that could result in more flights and fewer delays.
But Juliet Kennedy, Nats operations director, said: "What is needed is a clear and stable UK policy that recognises how important our airspace is as a critical part of our national infrastructure.
"It is essential that we are able to balance the needs of airspace users with the environment and, of course, with the communities who experience aircraft noise."

Daimler, which owns the luxury car maker, has been under intense pressure from police and prosecutors.
Authorities are investigating the possible manipulation of diesel exhaust emissions in passenger cars.
A Daimler spokesman said the software fix, which will cost about 220m euros (Â£195m), was not linked to the police investigation.
He said the "voluntary service measure" was to cut nitrogen oxide pollution.
"The service actions involve no costs for the customers. The implementation of the measures will be starting in the next weeks," Daimler said.
The measures come after German MPs last week questioned Mercedes-Benz executives about emissions.
At the time the carmaker agreed with the transport ministry to undergo another round of emissions tests.
In May German police searched 11 offices of the carmaker as part of an investigation into possible fraudulent emissions data by employees.
A total of 23 prosecutors and 230 police officers took part in the search in the states of Baden-Wuerttemberg, Berlin, Lower Saxony and Saxony.
Air traffic controllers are warning that UK skies are running out of room for record numbers of planes.
[NEXT_CONCEPT]
Three million Mercedes-Benz owners in Europe will be offered a software fix for their diesel cars.