Someone whose childhood did not involve a lot of Disney, those Mickey ears are a constant source of amazement.

It starts on the coach ride to the port of Barcelona, when a collective shriek goes up as soon as they appear in sight.

Disney certainly knows a thing or two about what children like, and the big black ears take pride of place on the top deck of the Disney Magic, the elegant art deco-style ship on which we are to spend a week cruising the Mediterranean.

Disney’s fleet of four ships, whose itineraries include the Caribbean, the Bahamas and Alaska, are wildly popular and our sailing sold out months in advance.

The Magic, the first to launch in 1998, has recently undergone a major refit. The prospect of being invited on board, to see what Disney Cruising is all about, made the heads of my four-year-old and two-year-old spin.

There are staff everywhere, intent on engaging with the children, but my youngsters are keen on some lunch before a deck party to celebrate our departure from dock – an energetic affair complete with Mickey and his mates and lots of enthusiastic dancing and singing. Even the confetti that rains down is in the shape of the, by now ubiquitous, ears.

Both children have slightly maniacal grins on their faces, while I'm giving thanks for the Perspex-lined railings making it near impossible for even the most agile toddler to debark ahead of schedule.

The cabins are lovely. Designed for families, they are spacious and well-appointed with loads of storage, and bathrooms split into a separate toilet and bath/shower areas.

By the pools, the deck's been ripped up and replaced with new water play areas and the AquaDunk, a three-storey slide with a near vertical launch through a translucent tube that extends 20ft over the side of the ship.

Dining on board is a real pleasure. Disney Cruise Line runs a clever rotational system that has guests eating dinner at all of the three main restaurants, but with the same two servers every night.

Our servers, Andre and Cornel, were wonderful with the children, learning their likes and dislikes and remembering to bring us a glass of warm milk to take back to the cabin each evening.

I dined on sea bass, lamb cutlets, tiger prawns and, on the final night, two baked lobster tails on account of enjoying the first one so much Animator’s Palate is my children's favourite restaurant, on account of its black and white theme that becomes slowly more colourful as the evening goes on.

But there are also lots of adults-only areas in the form of bars and the excellent Palo restaurant, safely tucked away on the top deck where a late-night drink can be taken with not so much as a “Mummy, can I...” to be heard.

But that’s not what we’re here for, obviously.

Our days promptly become a whirl of kids' clubs, half-day excursions to Nice and Pompeii, swimming, eating and meet and greets with Disney characters. Their appearances are scheduled but you are just as likely to come across Goofy exiting the lift.

The kids' clubs, grouped into age groups with staff on hand to facilitate activities, are a focus of the refurbis hment, with Marvel's Avengers Academy providing an area where children can “unleash their inner super heroes” by building up skills over the course of the cruise. Adjacent to Marvel’s is Andy's Room, where stars of the Disney-Pixar Toy Story trilogy include a larger-than-life Mr Potato Head, a giant version of the piggy bank Hamm and a Slinky Dog slide.

Next door is Pixie Hollow, home to Tinker Bell and her friends, where her teapot house serves as a costume wardrobe.

While the children are honing their new talents, a refurbished spa offers adults everything from teeth whitening to barbershop services, while the new Chill Spa provides treatments for teens aged 13 to 17.

Despite the full days followed by dinner, and on one occasion a spot of rock'n'roll dancing with 50 or so other toddlers who crashed the dancefloor en route to their cabins, the absolute highlight for my children was the evening show.

The performance on the final night, the West End-standard Disney Dreams about a young girl desperate not to lose her imagination, featured Tinker Bell lighting up the theatre with fireworks and some cracking song-and-dance routines from the best films of the past 15 years.

After bubbles and snowflakes rained down from the ceiling, a screen showed Tinker Bell spreading a little pixie dust over the bow of the ship as thousands of fairy lights lit up the theatre.

As my daughter breathlessly said on her return home: “Tinker Bell was there and she lit up the whole ship. She magic-ked the whole ship.”

Josie Clarke was a guest of Virgin Holidays Cruises (virginholidayscruises.co.uk; 0844 573 4398) who offer
the seven-night Disney
Magic Med Cruise from £949 per adult and £699 per child. Departs from Barcelona,
calling at Villefranche (for Nice, France), Pisa, Rome and
Naples, including flights from London Gatwick and transfers. Prices are per person based on two adults and two children travelling and sharing an inside cabin on a full-board basis. Based on a departure on August 30, 2014.