I stand ogling an extravagant cascading chandelier in the lobby of Regent Seven Seas’ first new vessel in 13 years – the much-anticipated Explorer. It’s just one of 473 light fittings sourced from crystal artisans in Sweden and the Czech Republic. Together with an acre of marble, and more than 2,000 artworks (including original Picasso plates and a Chagall sketch), it’s a reminder of why the ship has been billed as ‘the most luxurious ever built’. The all-suite, all-balcony cabins come with thick carpets and silk-stitched quilts: the Regent Suite, the largest on board, has a Dakota Jackson-designed Steinway grand piano and a £68,000 Savoir mattress.

For dinner on the first night of my Rome to Lisbon voyage, I head to Chartreuse, one of five fully inclusive restaurants. Designed by New York-based studio ICRAVE, it has coloured-glass panels, metal latticework and gold leaf mosaics.

Edith Piaf’s ballads play softly in the background as I sip a glass of Sancerre and work my way through savory souffles, poached artichoke, roast lobster and plump pistachio macaroons. In Italy, I escape Florence’s selfie-stick ridden piazzas by crossing the Arno River to the tranquil Bardini Gardens, where sandstone figures hide beneath cloaks of wisteria and climbing roses. In France, I swap Monte Carlo’s manicured streets fora stroll along pebbled coves sheltered by the pine-scented cliffs of Cap d’Ail.

A stonewalled labyrinth of lanes carved with Hebrew inscriptions causes me to linger in the medieval Spanish town of Girona, and I take a peek inside Salvador Dali’s bewildering Theatre Museum in Figueres, where a circus of dripping clocks, jewel-clad lips and surrealist oddities gather beneath a geodesic dome that rises from the remnants of a burnt-out theatre. Truth be told, many guests seem content not to disembark.

There’s a surprise lurking around every corner, be it the leather-floored library or the Connoisseur Club with its rare cigars. Idling on the pool deck where chunky loungers are shielded by gauzy drapes, it feels more pared-back beach club than cruise ship. Hearing whispers of a secret spot squirrelled away in the Canyon Ranch SpaClub, I decide to investigate. On a slip of aft deck scattered with love seats there isn’t a soul to be seen, so I wade into the infinity pool and forgo lunch in favour of surveying Barcelona’s skyline from afar. After all, there’s always room service.