Strolling along the leafy, sun-dappled paths of Majorca’s Hotel Barceló Formentor, taking in the majestic sweep of the private sandy beach and glorious views of the sea, it was difficult to escape a powerful impression of having been here before – which in a sense I had.

The environs of the Formentor, an establishment in the grand luxe tradition celebrated across Europe, played a starring role, unforgettable to those of my generation, in the 1982 screen version of Agatha Christie’s Evil Under the Sun.

The dapper Belgian detective Hercule Poirot exercised his little grey cells in the same bosky bowers, in the unlikely shape of Peter Ustinov, an actor large and shambolic rather than bijou and precise.

Sir Peter, a noted polymath and gourmet, savoured the hotel in a private capacity too. Poirot’s creator Dame Agatha was an enthusiastic visitor as well. She was among many 20th-century icons who favoured the place, including Winston Churchill, the Duke and Duchess of Windsor, Prince Rainier and Grace Kelly (they honeymooned there), Charlie Chaplin, Audrey Hepburn, John Wayne, Laurence Olivier and – inevitably – Aristotle Onassis and Maria Callas.

It will be seen that every one of these (except perhaps Wayne) was noted for an appetite for luxury and glamour that the privately owned Formentor provided – still provides. Many of them too (again I except Wayne) possessed artistic and intellectual leanings central to the hotel’s ethos.

As two members of the Barcelo family write in the Formentor’s history: “Formentor became a place where the best creators, the best artists, the leading figures of the 20th century, gathered to debate, think, have rest or simply live in a unique privileged enclave that encouraged them to reveal and discover the best of themselves.”

And still they come – some these days under the umbrella of Formentor Sunset Classics. Set up in 2013, this annual festival of outdoor concerts features international stars and younger artists certain to be following them to the top in the years ahead.

Among past participants have been Daniel Barenboim, Zubin Mehta, Kiri Te Kanawa and pianist Lang Lang.

As the 2015 season wound up last October, with a sensational performance by the American baritone Thomas Hampson, I was among those privileged to be present at this truly fabulous occasion.

Preceded by a glittering champagne reception on the terrace of the hotel, and followed by a gala dinner in the beachside restaurant, the concert provided a thrilling demonstration of the artistry and versatility of the singer.

The repertoire ranged through opera, operetta and musical theatre, taking in some of the roles that have brought the singer huge acclaim in opera houses across the world.

They included those of Germont in Verdi’s La Traviata, whose affecting aria ‘Di Provenza il mar, il suol’ was a highlight of the night, and Rodrigo, friend to the prince in the same composer’s Don Carlo. Wonderful tunes by Franz Lehár, Leonard Bernstein and Cole Porter featured in the lighter side of the programme, which was punctuated by overtures, interludes and the like performed by the Balearic Symphony Orchestra under conductor Felipe Aguirre.

My journey to Majorca – a first for me – involved an early morning flight with Monarch – so early. indeed, given the coach service timings from Oxford, that there was little point in going to bed.

From the airport, our small party enjoyed a taxi ride of an hour or so through the island landscape before descending through mountainous terrain to the Formentor.

Positioned on the northern tip of the Serra de Tramuntana, a Unesco world heritage site, the hotel itself is a thing of beauty, built in 1928 for Argentinian Adan Diehl who intended it as a striking work of art.

Having checked in, I was escorted from the marble floored reception towards my luxury room where a very large bed, with many more pillows that one might reasonably expect, suggested the inviting prospect of a much-needed sleep.

This, indeed, occurred through the afternoon, but first came a press conference with Mr Hampson, at which he spoke lucidly and warmly of his craft, and, immediately following, a first taste of the Formentor’s superb cuisine.

Lunch was in Las Palmeres restaurant, where I enjoyed clam and monkfish risotto in a delightful garden setting overlooking the hotel’s large pair of swimming pools, still busy even so late in the season. Other guests were on sun loungers beside the sea, or wind-surfing, scuba-diving, sailing and riding – there is no shortage of activities for the active. Or the inactive – a long and relaxing massage was in store for me the following morning.

A lengthy exploration of the lovely grounds, had followed my siesta, stirring my appetite for dinner, which began in my case with pea risotto and burratano cheese, continued with lamb loin and concluded with creamed white chocolate and raspberries.

Naturally even this was outclassed by the gala dinner which supplied a climax to our visit: Norwegian lobster cannelloni with S óller shrimps and caviar, then tenderloin Angus steak with chestnut polenta and finally Granada pear and chocolate crumble and white truffle sauce.

Much delicious wine guaranteed a blissful night of sleep, after which it was up with the lark for the flight from dream to reality.