Security were reportedly spotted rushing over to a group of travellers who had gathered near the airline’s check-in area after one man became agitated and started yelling at staff in Italian, asking for someone to help.
The incident comes as Wizz Air customers say they have been supplied with helpline numbers that do not work after their flight was axed this morning.
Passengers booked with easyJet, British Airways and TUI Airways were also among those who have seen their plans to return from half-term or bank holiday breaks disrupted.
The aviation industry is struggling to cope with the rise in demand for travel amid a severe staffing shortage.
Rosie, 28, had travelled to Gatwick from Bognor Regis with her husband and two young children, who are two and 18 months old, and were booked on a Wizz Air flight to Catania, where her husband’s family live.
She said: “His family haven’t met our two children yet – because of Covid we haven’t been able to get out there, and I’ve been pregnant so haven’t been able to go. We wanted them to go and meet his family.
“The whole time we were told our flight was running on time, we then got told our flight was delayed by an hour. We then came to the gate, we all got ushered into the gate group to be told the flight was cancelled and that we need to come here and we’d be supplied with a hotel room and a substitute flight.
“There has been no communication, we’re only getting told now by Wizz Air that our flight’s been cancelled, and it was already meant to be up in the air.”
The couple have tried on previous occasions to travel to Sicily with other airlines, including easyJet, and had those flights cancelled too.
She added: “There’s zero communication, we’ve got small children and there’s people here who don’t speak English, there’s no help.”
Emma and Kevin Wood, both 51 from Hampshire, had also planned to fly to Sicily with the airline on Monday morning.
Mr Wood said there had been “no help at all” from the airline, with Mrs Wood adding: “They just said basically said try and rebook it online or on their website.”
Mr Wood said: “They’ve been saying there’s been issues (with flights) but we were hoping since the holiday weekend was finished that things perhaps have calmed down a bit, but clearly not.”
The couple were given a number to call for further support, which they said “didn’t seem to work”.
Wizz Air has been approached for comment.
Some 225 departures from UK airports were cancelled between Monday and Friday last week, according to aviation data firm Cirium.
That compares with 24 during the corresponding half-term week last year.
Travel consultancy The PC Agency estimated that at least 15,000 passengers were affected by “last-minute changes” to flights on Sunday.
Chief executive Paul Charles said this caused “major knock-on effects” and “it will take three days to clear the backlog”.
UK airline passengers have been hit by disruption for several months due to a lack of staff after letting thousands of people go during the coronavirus pandemic.
Airlines, airports and ground handling companies repeatedly called for sector-specific financial support during the Covid-19 crisis as Government travel restrictions suppressed demand. They are now struggling to recruit new staff and have their security checks processed.
Transport Secretary Grant Shapps has rejected calls to open the door to more “cheap” overseas workers in a bid to relieve the pressure on the aviation sector.
Asked whether he would temporarily allow more foreign workers into the industry to alleviate staffing pressures, told the BBC’s Sunday Morning programme: “The answer can’t always be to reach for the lever marked ‘More immigration’.
“There is not some pull that is going to relieve this.”