For two millennia, the citizens of Budapest have nursed a passion for bathing. Far beneath them, in geological fault lines, is a watery cauldron, the source for more than 120 thermal springs, with temperatures ranging from warm to scalding.

These waters have produced an obsession. It began as a pursuit of health. It became a pursuit of pleasure.

To the people of Budapest, the bathhouse is what the pub is to the English or the coffee house is to inhabitants of American sitcoms. Stripped off and immersed in communal pools, they come to meet friends, to chat, to read the papers, to play chess, to catch up on the gossip.

Rather than a couple of lagers, a bag of salted peanuts and a bluff landlord, the bathhouse has steam chambers, hot pools and a vigorous masseur. Some people kick-start their day there. Others come after work to unwind. For others still, it is the mid-afternoon pick-me-up. I bought a swimming cap, a pair of flip-flops and a bath towel, then set off into the city’s water world.

In the vaulted entry halls of the Rudas baths, Attila the Accountant helped me to decipher the bewildering list of options on the tariff board above the ticket kiosk: balneology treatment, physio-massage, pedicure, manicure, aroma massage, Thai massage, underwater massage. I was a bath novice.

Attila recommended starting small – bath and massage. “Why make complicated what God made simple?” was what Attila said. It was bathtime rush hour, 6pm, and groups of men clutching towels filled the hall. Under Attila’s guidance, I passed through the turnstiles, where a whitecoated attendant handed me a key and a small white apron.

The key was for a locker, where I left my clothes; the apron was to wear in the bath. It was a fetching garment, a miniature pinny that just covered one’s willy while leaving the buttocks exposed.

Feeling a trifle self-conscious in what could be mistaken for a male stripper’s show costume, I proceeded to the main baths, pausing for the obligatory shower.

In the central chamber, I seemed to slip through a time warp, perhaps to the 1st century AD and the court of Caligula. Clouds of steam parted to reveal men strolling about in their toga-like aprons. An eerie mix of sounds – voices, water dripping and splashing, flesh being slapped – echoed beneath the dome above us, from where pinpoint shafts of light slanted through the steam. In the large central pool, men lounged in the water, only their pink heads breaking the surface.

Beyond fat pillars were more pools and more floating heads. I lowered myself into the water and stretched out. It was blood temperature, and deliciously soothing. I felt myself relaxing into its warm embrace, or at least as much as I was able to relax, cheek by jowl, so to speak, with a lot of hairy men wearing nothing more than a loose posing pouch.

The head of Attila the Accountant appeared out of the clouds of steam. He leant back next to me against the edge of the pool. “It is question of perspective,” Attila said, gazing dreamily up towards the dome. “In bath, nothing seem too bad ... You can be bankrupt. You can be murderer. But here you forget your problem.”

He sighed, cupping his hands behind his head. “Who knows? Who cares?” was what Attila said. In the corners of the main chamber were other pools – warm, tepid, cool, cold. Beyond were saunas and a steam room. Then more showers, where we could abandon our pinnies for long, white sheets that made us look like Roman senators gathering to assassinate Caesar.

The masseur was waiting for me in the gloom of cubicle five. He was a bald, malevolent-looking fellow, reminiscent of those East European weightlifters, pumped up on drugs and propaganda, who regularly beat western waifs to the medals during the cold war. Relieving me of my cotton sheet with a flick of his wrist, he waved me onto the table, then began to work on my naked form. It was excruciating.

I didn’t have the Hungarian for “Easy with those thumbs”, so I tried audible wincing. He took the resulting noises for expressions of pleasure and redoubled his efforts. It didn’t help that he was engaged in a heated argument with the masseur in the next booth. As voices were raised, the massage degenerated into a kind of GBH.

He took out his anger on my back, pummelling me with a series of combination punches, right, left, right. When he had finished, I crept away to the relaxing room, where I lay, rather gingerly, on a recliner beneath ancient brick vaults.

THE RUDAS BATHS are originally Turkish, but the bathtime story of Budapest goes back further than that. The Romans began the tradition with thermal baths for arthritis. Sufferers came from across the empire.

And Roman baths extended the cure beyond specific complaints. The slow rituals of hot and cold, of massage rooms and steam chambers, were a pleasure in themselves, and that pleasure was deemed central to physical and mental wellbeing.

When the Huns invaded – led by the accountant’s namesake – they screwed up the plumbing, and bathing in Budapest fell into one of its periodic declines. There was a limited revival in the Middle Ages, when the church got into the business of promoting thermal baths, though for medicinal purposes only.

Not for the clergy the idea that lounging about seminaked was good for the soul. In general, it was a time when Europeans and soap and water were strangers. Isabella of Castile was able to boast, in her old age, that she had bathed only twice in her life.

The Turks reintroduced serious bathing when they conquered the city in the 16th century. They remained for 150 years: plenty of time to build elaborate bathhouses and encourage the locals to join them for a hot soak. The next day, I set off for the Szechenyi baths.

Beyond a curving drive and a formal garden of box hedges, the grand yellow facade of the bathhouse loomed through the autumn trees, a veritable palace of bathing: a multi-domed, neo-baroque creation built at the beginning of the 20th century, with the overblown architectural aspirations of the 19th.

Inside was an institutional world of chits and treatment rooms and white-jacketed attendants. It felt like a Soviet health farm, if Soviet health farms were friendly and inviting. Szechenyi is mixed – the tiny aprons here replaced by swimming costumes – and the presence of women seemed to lighten the atmosphere. In the two inside pools, shafts of sunlight fell from high windows onto the bathers’ upturned faces.

But most people were outside in the courtyard. Szechenyi’s outdoor pools are to bathing what La Scala is to opera. This is its grandest setting, an amphitheatre of colonnades and statuary. Here, even in the depths of winter, as snow settles in the crevices of the statues, ardent bathers are to be found in the steaming water.

I settled into the 38C pool, beneath the statue of a naked woman getting carried away with a swan, and felt the tension in my limbs, still recovering from the attentions of the Rudas masseur, uncoil. All around the pool, bathers lounged like hippos. Some read newspapers. One man was deep in a Russian novel.

Another was smoking a pipe. A young couple lay entwined, while at the far end an older couple seemed to be discussing their divorce. A group had gathered round two fellows playing chess on a floating board. The rest of us gazed dreamily into the middle distance, in the warm embrace of the waters. We might have been strangers, but we had found a curious communality. We were having a bath together, and it had come to seem the most natural thing in the world.

The following day found me back on the other side of the Danube, at the Gellert baths. Opened in 1918, the building is an art-nouveau masterpiece. The domes, the mosaics, the fountains trickling, the shafts of light slanting, the strange aqueous acoustics, all conspire to lull you into a watery trance.

There is a sense that the world has slowed to half speed amid the murmur of voices and the lap of water. My thoughts drifted with the steam, going nowhere in particular. The Gellert was like one of those congenial cafes where you sit over your half-empty cup, watching the world go by. Except here, the world was in bathing suits.

I hadn’t planned to stay long. There were other things to see in Budapest – the Danube, the Royal Palace, the medieval streets, the crazed drinking habits of the descendants of the Huns – but an hour later, I had hardly stirred. The baths were becoming my drug, and I was becoming addicted.

Had I arranged to see someone for lunch? What did Attila say? “Who knows? Who cares?” In the bath, you forget everything.

Stanley Stewart was a guest of British Airways Holidays

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