I caught up with the group of around 1000 refugees leaving Budapest on foot as they were crossing the Danube on the Elisabeth suspension bridge. We walked west along a dual carriageway. Families wheeled their belongings in pushchairs, with babies teetering on top. People were in flip-flops and beaten-up loafers. A woman pointed at my walking boots: ‘Very good,’ she said. Hungarian drivers stopped to offer people water and food. One man gave a family two pushchairs. At service stations, attendants rushed to the doors to stop people from entering, though they handed out bottles of water. A man on crutches overtook me, his friend carrying his prosthetic leg. It was about 150 miles to Vienna.

‘When will they send buses for us?’ a man carrying a faded Adidas sports bag on his shoulders asked me. His two friends leaned in. ‘I don’t know,’ I said. ‘They sent buses yesterday.’ He told me his name was Marwan al Chami. They came from Homs, where his wife and two-month-old son still were; the rest of his family were in a refugee camp in Lebanon. The crossing from Turkey was very dangerous, he said. ‘We had babies and a pregnant woman in our boat.’ An Italian navy ship rescued them off the coast of Kos. After crossing the Serbian-Hungarian border, they were offered a lift to Germany, but the driver dumped them after ten miles, driving off with their €1200. Marwan hopes his family will join him in Germany. ‘They fly, not walk,’ he said.

After about an hour, the police directed us onto a smaller road that took us through the Buda hills’ outlying towns. ‘How many hours to Vienna?’ asked Iham, a young Syrian man in a baseball cap. ‘About four days,’ I said. He nodded solemnly but then, pointing at his friend’s formal leather shoes, laughed: ‘Crazy man! He walks from Damascus.’ They were heading for Munich. Iham ran after people picking up the rubbish they’d dropped. ‘Very bad,’ he said. One of the most popular stereotypes Hungarians had of the refugees was that they were dirty and didn’t tidy up after themselves.

At a roundabout in the small town of Budaors, Hungarian families had laid out hundreds of bottles of water, packets of biscuits, boxes of fruit, piles of clothes, nappies, toilet paper. Young men rushed towards them, scooping up armfuls of whatever they could; other people shouted at them to be calm and polite. Parents tried different shoes on their children’s feet before rushing on. A man offered a packet of biscuits to two young Hungarian girls standing on the roadside with their mother, who blushed. We rested in Budaors for half an hour. I spotted Marwan and he asked me to sit down. He’d taken his shoes off and was rubbing his ankle. ‘Problem,’ he said, looking at his foot and shaking his head. We’d walked about ten miles.

The police stopped us when we reached a junction with the motorway to Austria. They said buses were coming and urged us not to walk on the motorway. People stretched out on a grass verge and waited. A Hungarian volunteer showed children how to ride her bicycle. I saw Marah, a 20-year-old Syrian woman I’d spoken to earlier. I told her buses were coming. ‘Really?’ she said, and went to tell her family. She came back with five train tickets: ‘They are from Budapest to Munich. Please take them.’ I said I couldn’t and they might still need them. ‘Do you think we’re poor?’ Marah asked. Her father had been a pharmacist in Saudi Arabia and she’d been to an American school there. Their home, Aleppo, was 90 per cent destroyed. ‘Every day they say that Isis would attack the city. We waited for five years for the war to end and it didn’t end.’

The buses didn’t come, so we kept walking, now on the motorway. By 6.30 it was getting dark and the sky was clouding up. We walked passed empty industrial estates and a giant Aldi distribution centre. Hungarian TV crews drove in cars ahead of us, the cameramen sitting in the boots. People were angry at the police now. ‘We want bus!’ the crowd shouted and blocked police cars that were trying to get past. We’d walked about 15 miles out of Budapest when we reached the outskirts of Biatorbágy, which had a railway station with trains bound towards Austria.

People abandoned their pushchairs outside as they rushed into the station. ‘The first train is not for you,’ the police said, as they tried to form a cordon along the platform edge. People rushed across the tracks to the other platform when a train came in (bound for Budapest). Several of them narrowly missed being hit by an express train that sped through the station, its horn blaring. Downstairs, Hungarian volunteers handed out water and bread. ‘You are coming with us?’ Iham asked me. I said I would go back to Budapest once they were on the train.

After an hour, a train going to Győr, about 25 miles from the Austrian border, pulled in. Hungarian volunteers shouted for women and families first. People rushed for the carriages nearest to the stairs. ‘Down here,’ I shouted to a family trying to get into one of the overcrowded carriages, pointing further along the train. It left at 8.30, the volunteers and press waving as it pulled out of the station. When I got back to Budapest, I emailed Marwan and Marah, asking if they’d got to Austria. I didn’t get a response. News reports that evening said that 8000 refugees had crossed the Austrian border by train, bus and foot.