In the busiest summer ever for UK aviation, airlines are extracting maximum revenue by selling seats that don’t exist - and then flouting European rules on overbooking.

Britain’s biggest budget airline, easyJet, is overselling thousands of peak-season flights, breaking up family groups and telling some holidaymakers who bought tickets months ahead they must travel by circuitous routes to reach their destination.

The tennis player, Annabel Croft, tweeted from the Algarve: “Have arrived Portugal minus our daughter. Not a great start to our family holiday - no idea buying a ticket didn’t guarantee a seat. I asked easyJet if I could stay with her and they said yes, but we will charge you £60. Unbelievable.”

No attempt was made to persuade other passengers to take a later flight in return for cash or travel vouchers, even though EU passenger-rights stipulate airlines must seek volunteers.

An easyJet spokesman said: “Unfortunately this process wasn’t followed in this particular case and this issue is being addressed with the ground team who looked after that particular flight.”

European regulations also require airlines to get offloaded passengers to their destination “at the earliest opportunity”. Accordingly, Mr Whelan asked for his sons to be booked on the next available British Airways flight from Heathrow to Barcelona. But easyJet refused, insisting they must fly 32 hours later from Bristol.

The airline describes the flight on the evening of 19 July from an airport 120 miles away as a “reasonable alternative” to the 18 July morning departure for which they had tickets. So Mr Whelan paid £640 to book seats on the BA flight from Heathrow, and £45 for a taxi from Luton.

Mr Whelan said it appeared more than half that day’s flights from Luton were overbooked; a departure to Amsterdam was oversold by 12 passengers. He described his treatment by easyJet as “truly shocking service - honestly the worst I've ever experienced, and I've travelled widely.”

An easyJet spokesman said that 2.6m of their passengers each year fail to turn up for booked flights. (Getty Images)

A spokesman for the airline said cases of denied boarding due to overbooking were “extremely rare”. He said 2.6m easyJet passengers a year fail to turn up for booked flights.

“A flight will only be overbooked after reviewing the no-show rate for the last three months. On average, across our flights we will only overbook by one or two passengers per flight.”

European legislation stipulates that anyone denied boarding against their will must be paid immediate compensation - ranging from €250 for short flights to €600 for long-haul trips. But Ed Thompson, a photographer from Kent, was denied boarding for an easyJet flight from Gatwick to Greece in June and says he has still not received compensation despite repeated requests.

Citing “better-than-expected revenue per seat,” easyJet has raised its profits forecast to around £640m for the year ending in September.

British Airways failed to follow EU rules when it overbooked a BA flight to Split in Croatia. Hilary Owen from Buckinghamshire had a confirmed booking. But at check-in at Heathrow she waited in vain for two hours, finally being told she would travel the following day via Zagreb. The airline initially refused to pay for her taxi home, with BA Customer Services telling her: “We are unable to settle your claim for alternative travel expenses.” After The Independent intervened, the airline agreed to meet the cost.