As I sit on deck polishing off a truffle omelette for breakfast, glance around at the private superyachts berthed next to us in St Bart’s harbour, set against a backdrop of lush palm trees and a deep blue sky. It’s easy to forget that I too, am not part of this elite club on my own private yacht. Instead, I’m on the next best thing: Sea Dream II, a 112-passenger yacht owned by Norwegian entrepreneur Atle Brynestad (he also owns Sea Dream I, the ship’s sister vessel), which sails the smaller, more authentic, French Grenadine islands of the Caribbean.

Every island has such individual character, so the best way to tick off a handful is by boat. We tour the beautiful volcanic island of St Bart’s – which was discovered by Columbus in 1493 and named after his brother Bartolomeo – on quad bikes, losing a few stragglers to the lure of Nikki Beach and Hotel Eden Roc, before heading to the effortlessly cool Do Brazil beach bar and restaurant on the more relaxed west coast. Co-owned by French former tennis star and singer Yannick Noah, it’s the ideal place to laze away the day. Laid-back Ibiza-inspired tunes play over the sound system as we feed on mouthwatering ceviche, washed down with glasses of ice-cold rose.

What’s brilliant about this boat is that when anchored, you can jump straight off the back of the deck to swim, or take a turn on the hugely popular jet skis. The daily changing menu is unexpectedly grand, with decadent dishes such as venison Wellington and gold leaf-topped chocolate fondant served up with Downton Abbey-esque service.

This is fine dining at its absolute best so the format at meals is quite formal; afterwards, kick back at the bar where resident mixologists are on hand to whip up cocktails based on your favourite flavours. The cabins themselves are not high spec but weather permitting, it’s fun – for one night at least – to sleep on a daybed on deck. When the skies are clear, there’s something deeply magical about being out under the stars. And it’s another way to dream, just for a while, that this is your very own private yacht.