Stepping into the lobby of the Gellért Baths in Budapest is like stepping back in time. Having resisted the temptation to look at photos of the baths online, I was thrilled at my first sight of the spectacular art nouveau interior.

After changing, my husband and I did a few laps of the main indoor pool, admiring the intricately decorated columns surrounding us. Afterwards, we explored the building’s labyrinth of geothermal pools before emerging on to the enormous roof terrace. There, we swam in the heated outdoor pool under bright sunshine.

Less touristy than the more party-style Széchenyi Baths, the Gellért offered us the chance of a decent swim and steam.

Visiting a thermal spa in Budapest is a must, but this wasn’t the first dip on our Interrail trip around Europe last spring. Lured by the offer of a discount on an Interrail Global Pass, we found time to travel across mainland Europe by rail – 30 years since I last Interrailed in my 20s – with little in mind but sightseeing, eating and drinking.

We had loosely planned a clockwise route, starting on the Eurostar from London to Brussels and returning via Paris two months later. Staying in mid-price hotels and hostels, we took whirlwind tours of Bruges, Brussels, Hamburg, Copenhagen, Berlin and Kraków, trying an endless stream of cafes, bars and restaurants.

But less than two weeks into our trip, when we arrived in the Slovakian capital, Bratislava, we found that our experiences were already blurring into one. What’s more, despite walking a good number of steps each day, we were feeling the effects of the freedom to overindulge and missing the routine of our regular swims back home.

So, deciding it was time to take action, we hit on the idea of seeking out a swim wherever we stopped. We Googled swimming pools and set off across the city on foot, eventually arriving at Plaváreň Pasienky. Once inside the facility’s largely deserted building, we wandered up and down staircases and along quiet corridors until we spotted a sign telling us that the entrance to the pool was “through the wardrobes”. We located our respective changing rooms and found an attendant selling tickets.

Our journey through the wardrobes then led us to a 50-metre pool – the largest in Bratislava – with just a handful of swimmers bobbing along the lanes. Though the pool was a little run down (and would soon be refurbished, to reopen this spring), we emerged feeling invigorated and ready for the next leg of our journey.

Besides the obvious physical benefits, our swimming expeditions also took us to parts of cities we might otherwise have missed.

On our way to Plaváreň Pasienky, we chanced upon the giant Slovak Radio Building, shaped like an upside-down pyramid. After our swim, we travelled back to the old town by trolleybus, missed our stop and ended up at the parliament building, where we dined at a restaurant overlooking the Danube.

In Budapest, our visit to the Gellért Baths had led us across the Danube from Pest to Buda via the magnificent Liberty Bridge and given us glorious views over Gellért Hill.

As we journeyed across Europe, we became obsessed with comparing swimming pool prices and facilities, embraced the array of wristbands and tokens for lockers and hairdryers, learned that most pools insisted on flip-flops and a swimming cap, and came to accept the lack of information online about opening times.

In Austria, during our stay in the south-eastern city of Graz, we swam at Bad zur Sonne, a pristine stainless steel-bottomed pool where the efforts of swimmers contrasted starkly with spectators enjoying an early morning beer. Later, our swim provided a conversation opener with locals, who told us how, before the building was renovated, it had been the scene of an arts event, with bands using the drained pool as a stage and artists setting up their wares in the cubicles.

A rainy day in the Slovenian capital, Ljubljana, led us to the 10-lane Kopališče Tivoli in Tivoli Park where, after our swim, we ate delicious savoury waffles in the pool’s Vafljivaflji cafe and drank fresh orange-and-mint tea. Our exit through the park led us to an outdoor photographic exhibition, an ornate Serbian Orthodox church and the Museum of Modern Art, with its fabulously stylish cocktail bar.

In Trieste, we walked the width of the port to the enormous Centro Federale, run by the Italian Swimming Federation. After a patient receptionist helped us register online, we made our way around the building to Piscina Bruno Bianchi. We were about to jump into an empty Olympic-size pool when we spotted the teams of swimmers arriving for their competition and noticed a smaller pool at the back for public swimming. With its six lanes and diving “pit”, the 25-metre pool was still an impressive facility.

The walk back to our Airbnb led us along the tree-lined Passeggio Sant’Andrea, where we stumbled on the Ariston cinema and watched an Irish arthouse film.

In Vicenza, we were sure we’d taken a wrong turn when we arrived at a building milling with teenagers, but a helpful student directed us across the school car park to Piscina Patronato Leone XIII. The facilities were basic but the pool was clean and orderly, thanks to an officious attendant who made sure everyone showered before getting in the water, and swam in the right direction.

In Pistoia, an underpass led us to a quiet residential area and, down a side street, to the grandly named Acquarama.

“Do you know the Olympic pool in London?” asked the receptionist, surprised to see tourists. We nodded eagerly.

“Well, this is nothing like that!” he laughed. When we saw the narrow pool with its faded tiles, we understood why he wanted to manage our expectations, but with only one lane already occupied we enjoyed another refreshing swim.

As we took the train along the Italian Riviera towards France and the weather got warmer, our swims moved outdoors, but we continued to look for modest locations.

On a fine day in Sanremo, we slipped on to the beach of Bagni Paradiso, where the rocky groynes and rows of changing cabins created the calm of a lido. As it was still slightly off-season, the only other visitors were inside the beach restaurant – guests at an Italian family lunch.

In Antibes we loved the unpolished feel of Plage de la Gravette – the horseshoe-shaped public beach behind the ramparts of the old town, made all the more entertaining by seasonal workers from the luxury yachts in the harbour, who shared stories as they swam in the sea.

In Bordeaux we took the tramway to Les Aubiers and serene Plage du Lac. We clocked up lengths while ducks swam around us and boats sailed by in the distance, rested afterwards under tall trees, watching teenagers playing table tennis – and felt we’d been fully immersed in local culture.