As 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 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 ship on which we are to spend a week cruising the Mediterranean.

Most of the mothers in my local circle, though well-versed in all things Disney, had no idea the company runs a sideline in cruises, but it turns out we're a little late to the party. The fleet of four ships, whose itineraries also 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, recently had 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.

I admit to a little trepidation, travelling on my own with two active and enthusiastic youngsters, but "the magic" of the experience, and consideration for the logistics of cruising as a family are plain from the moment we step aboard.

There are staff everywhere, intent on engaging with the children, but my youngsters are keen on 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 ubiquitous ears.

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

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

Following the re-fit, there's now more storage space under the beds and the colour schemes have been updated.

But some of the real excitement is up by the pools, where 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 about six metres over the side of the ship.

Most of the restaurants have had a makeover, and the ship's food is the real revelation. While Disney may not have always made this a priority at their parks, dining on board is a 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. My daughter, who discussed her day's activities with them every night, was genuinely sad to say good-bye at the end of the voyage.

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). I have officially forgiven Disney for any previous transgressions in the food department.

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 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.

At one point, my son turned and sprinted off down the corridor in hot pursuit of the mouse himself, demanding, "Stop, Mickey, stop!" Mickey duly stopped for a chat and a hug, and my little boy still talks about it.

Every staff member was extraordinarily happy to chat to children. The legendary Disney service apparently extends to their youngest guests, and the confidence it gave my children to wholeheartedly greet the staff and hold a conversation with them was lovely to see.

A particular favourite was Aileen, our state room host, who created towel origami every night in the form of a dog, dinosaur, swan and frog.

She and her colleagues became so popular that when my son's toy car rolled under the partition to the next room's balcony, he suggested that I "call room service".

The kids' clubs, grouped into age groups with staff on hand to facilitate activities, are a focus of the refurbishment, with Marvel's Avengers Academy providing an area where children can "unleash their inner superheroes" 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 and children can immerse themselves in art and craft activities.

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 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 – to gasps from every pre-schooler in attendance – 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 magicked the whole ship."

*The writer travelled as a guest of Virgin Holidays Cruises