How high can Carolyn McCall take easyJet before she bails out?

“I’m not going anywhere,” insists Dame Carolyn McCall, the chief executive of easyJet.

She might be trapped in a window seat on a flight to Italy, but the airline boss is not talking about escaping the journalists accompanying her to the opening of easyJet’s 27th European base, at Venice’s Marco Polo Airport.

Instead, Dame Carolyn is refuting speculation she could soon quit the budget airline. Rumours about her future have circulated since it emerged last month she was approached by Marks & Spencer about becoming its chief executive, a job she spurned.

One of Britain’s leading businesswomen, it is understandable she caught the eye of M&S. Since taking the helm at easyJet in July 2010, Dame Carolyn, 54, has been praised for her revamp of the no-frills airline.

Annual pre-tax profits have surged from £154m in 2010 to a record £686m last year, boosted by measures she introduced to grow lucrative business traffic and improve punctuality. Investors have cheered her work by sending easyJet shares flying from about 430p to £16.01, catapulting the airline into the FTSE 100. But despite Dame Carolyn’s achievements, she is not finished with easyJet yet.

“[M&S] approached me and I was not interested, I just want to stay at easyJet,” the airline boss insists, adding she will remain with carrier for the “foreseeable future”. Dame Carolyn concedes that if she felt “I couldn’t add any more value, then that would be the time to think about what next to do”. However, she believes there is still work to be done.

Last week’s trading update, in which easyJet reported a 3.7pc decline in revenue per seat for the final three months of 2015 as a result of the Paris terrorist attacks and suspected bombing of a Russian jet, show the airline, like the wider aviation industry, still faces challenges.

“The next three years, I think there’s just a huge amount to do on the digital side, the customer side,” the easyJet boss adds.

Furthermore, as well as launching routes and bases such as Venice, Dame Carolyn is busy dealing with the airline’s often combative founder, Sir Stelios Haji-Ioannou, whose family is the company’s biggest shareholder with a 33pc stake.

Sir Stelios, in the past a critic of Dame Carolyn’s pay, last week revealed he is pushing the airline to lift its dividend payout ratio from 40pc of earnings-per-share to 50pc. To express his dissatisfaction with the current policy, he will vote 5pc of his shareholding against the re-election of easyJet chairman John Barton at next week’s AGM.

But despite the founder’s latest broadside, Dame Carolyn insists the airline has a constructive relationship with its founder.

“I think it was important for him to let people know before the AGM his position on the dividend,” she says diplomatically.

easyJet’s new finance chief, Andrew Findlay, is currently reviewing the carrier’s balance sheet, which could give the company an opportunity to alter its dividend policy. But Dame Carolyn gives the impression she will not be bullied into changes if they might harm easyJet’s financial health.

“I wouldn’t assume anything until the outcome of that review and I think a 40pc dividend at this stage is a very high dividend,” she says. “I don’t think anything is more likely or less likely as a result of [Sir Stelios’s] statement. What we have to do is the right thing for the business.”

As well as handling Sir Stelios, Dame Carolyn must also fend-off easyJet’s rivals in the increasingly competitive low-cost airline market in Europe. Carriers such as Wizz Air and Vueling are looking to grow market share. However, analysts believe Ryanair, easyJet’s fiercest rival, poses the biggest threat because it is expanding at airports where the FTSE 100 airline has a strong presence.

Last month, Ryanair announced it would base aircraft at Belfast International, which Liberum analysts described as “another example of encroachment on easyJet’s network”. It follows similar moves by Ryanair at airports such as Milan Malpensa and Berlin. Nevertheless, the easyJet boss is unfazed by the challenge posed by the Irish carrier.

“We have a stronger customer proposition, much stronger than Ryanair, we have a much stronger digital experience,” she argues. “Remember, many airports in Europe are slot constrained at peak so [Ryanair] might move in but they won’t necessarily get peak slots.”

Like Ryanair, easyJet is in talks with long-haul carriers such as Germany’s Lufthansa about potentially becoming a short-haul feeder into their networks.

So-called interlining would undoubtedly transform easyJet’s business model. However, Dame Carolyn is cautious about the scale of the opportunity on offer, noting that many of easyJet’s passengers already “self-connect” by organising their own connecting flights.

“Unless there’s a simple way of doing it, it’s unlikely to happen,” she says. “We are reticent to do anything that would complicate our business.”

The easyJet boss also has much broader problems to consider. The spectre of a potential British exit from the European Union poses a threat to the airline, which flies to 137 airports, almost all of which are in Europe.

Although a vocal supporter of Britain’s membership of the EU, Dame Carolyn admits the airline has drawn up contingency plans in case the “Out” campaign triumphs in the looming vote. However, she refuses to share the details of the plans, adding: “Our focus is on Britain staying in."

With so much still on the horizon, it is no wonder Dame Carolyn insists she is not relinquishing the controls at easyJet just yet.