We stayed at Saints Constantine and Helena, next to Varna, which is actually Bulgaria’s oldest resort, a collection of holiday houses, private villas and hotels scattered through a mature park of magnificent tall trees – oak, beech, fig, poplar and cypress.

When the hot summer sun beats down, the ten-minute stroll to the beach through the cool, dappled shade of these trees is a pleasure rather than a penance. Saplings, tagged with the donor’s name and planted in the odd bare patch, commemorate the park’s centenary in 2008.

Quite a stretch of the immediate shore has been cordoned off by large hotels with private beaches. Primed by old hands at our more modest hotel, we made for one of the unspoilt rocky coves further along the coast.

In we waded; it was like Cornwall but much warmer – in fact, blissfully warm.

Further along again, people swam sedately in a mineral-water pool. ‘Taking the waters’ is popular in Bulgaria, with many hotels having both mineral and swimming pools.

Later that day – showered, dressed and respectable – we made for the cool, airy bar of the large Grand Varna hotel. We were refused a drink; we had no tag, we were not residents.

Neither could we book a table for dinner. The hotel’s ‘all-inclusive’ deal which bars outsiders must also stop residents trying the small, cheerful owner-run restaurants, coffee shops and bars that, along with a colourful medley of stalls selling fruit, toys, clothes, paintings and postcards, line the glades and leafy lanes that wind through the trees to the sea.

Golden wonder: Varna’s dramatic Assumption Day Cathedral is a sign of the city’s rich past

We chickened out of the six-mile walk along the tree-backed beach to the old port of Varna. Instead, we bought a 24-hour ticket – using half one day, half the next – on the red double-decker Varna City Tour bus, a hop-on hop-off service that conveniently takes you into town from St Constantine.

Passing up the zoo, the aquarium, the dolphinarium and the Oriental market, we made for the city centre. The domes of the Orthodox cathedral gleaming in the sun, the dark red opera house and the sparkling fountain in the main square, the cafes, the book and bric-a-brac stalls under the trees – it made an exotic and appealing picture.

And Bulgaria can be exotic. In spite of the reminders of the crushing Soviet rule seen in the few abandoned, brutal buildings interspersed between Varna’s beautiful, often crumbling 19th Century houses, there is the occasional whisper of the unknown East.

You catch it too, in spite of the crowds, in the faded frescoes of the old Byzantine churches in Nesebar, a Unesco World Heritage Site close to Sunny Beach, the biggest resort on the coast.

For centuries conquerors and migrants – Greeks, Persians, Romans and Slavs – swept across Bulgaria, leaving behind churches, monasteries, mosques and well-preserved old villages.

Timeless sparkle: Dymphna found a pair of gold Nike earrings in the Varna Archaeological Museum

Yet this country, rich in history and natural beauty and bordered by Romania, Serbia, Macedonia, Greece and Turkey, is now best known for its sixth border – the Black Sea – a 235-mile stretch of sandy, safe beaches, coves, cliffs, a dozen or so resorts and Varna, queen of the Black Sea coast.

Although Varna is a thriving commercial and maritime centre, the beach is only a ten-minute walk from the traffic-free and attractive main square, alive with cafes and restaurants, walkers and talkers.

Simply take the wide, pedestrianised Boulevard Knjaz Boris I, past modern shops and tall old houses. Cross Primorski Park where old women, crocheting under shady trees, smile at but do not bother passers-by, and voila! There, stretching to St Constantine, lies the calm blue sea and the golden sand.

We had lunch at a seafacing beach restaurant – a classic Bulgarian salad of locally grown peppers, tomatoes, cucumber and grated cheese with garlic bread and a glass of wine, all for about £6. You’ll struggle to beat the price or the atmosphere in the Med.

One of Bulgaria’s greatest treasures, a superb collection of gold jewellery, much of it over 6,000 years old and discovered in 1972, is in Varna’s Archaeological Museum, an austere 19th Century building that used to be a girls’ school. Don’t miss it.