It was my last day at work before maternity leave and I was feeling a little under the weather. I’m a computer scientist and I was doing presentations in the office but, after lunch, I decided to go home early. Then I felt my first contraction.

My husband Richard and I stayed at home until my contractions were five minutes apart – we didn’t realise that, because this was my second birth, we weren’t supposed to wait. We don’t have a car so, when it was time, we ordered an Uber to take us to the hospital.

We had to wait 20 painful minutes for the Uber to finish its previous trip and arrive. I was having contractions the whole time and Richard was tracking the car – it was frustrating, to say the least. The taxi finally arrived and Richard, our two-year-old son, Sebastian, and I all piled in. Five minutes later, my body started to push by itself. I was trying to hold it back, but the labour had begun.

The taxi driver, Priesh, was amazingly calm and collected. He was telling me all about his wife’s birthing experiences, and advising me on how I should breathe. There was traffic on the road and, although I was pretty out of it, I knew we weren’t going to make it to the hospital. We decided to pull up outside a medical centre that, luckily, happened to be en route.

As soon as the taxi stopped, my husband ran to get help. Sebastian began to cry: he could see I was in pain. Richard returned seconds later with three doctors and a wheelchair, but by the time they arrived the baby was already crowning and I couldn’t be moved.

The next moment, I felt I had to push again, and the baby started coming out. The doctor helped me take off my trousers, and seconds later little Michael was born, right there in the front seat of the Toyota Prius. Everything happened so rapidly. The only thing between me and the car seat was a maternity pad.

Straight away, the doctors took me inside, where they cut the umbilical cord and called an ambulance. It was a clear October day in Manchester – with no rain for a change – but the air was slightly cool and Michael’s body temperature began to drop. To keep him warm while we waited for the paramedics, I put him under my T-shirt – there were no blankets.

About 10 minutes after the birth, while I was still in the medical centre and we were waiting for the ambulance, my husband scrubbed down the taxi. Luckily, Priesh had wipe-clean leather seats – he even managed to pick up other customers later that day.

I was 36 weeks and six days pregnant when Michael was born, meaning he was technically premature by one day. When he came out, he hadn’t cried much, so when the paramedics arrived, they decided to call another ambulance. They took Richard, Sebastian and the baby in one, so they could open up Michael’s airways; I had blood loss, and went in the other ambulance on my own. As we left the medical centre, the people in the waiting room applauded us.

Uber gave Priesh some money to deep-clean the cab, and later they reimbursed us the fee for the trip and sent presents for the baby.

I had left my clothes in the car, and the next day Priesh turned up with them, all washed, plus some gifts for the baby. Bless him – I’m pretty sure Richard gave him a five-star rating. Everybody was so kind – the driver, the doctors, the paramedics – I can’t thank them enough.

When I compare this birth to my first one, I actually think it was more bearable. The labour in the Uber was honestly more pleasant, and easier. My first birth took two and a half days – this one was over and done with in two and a half hours.

Our family and friends were shocked when we told them the story. The whole experience was intense at some points, of course, but I’m just so happy that everything ended so well. Thank God there were no complications.

Would I call an ambulance instead of an Uber next time? Probably, but I do think that this way it’s a nice story to remember. I’m glad it happened as it did.

• As told to Ellie Harrison.

Do you have an experience to share? Email experience@theguardian.com