Evie was about three when I first noticed how much she had absorbed from our family conversations about politics. “Let’s play parties,” I overheard her saying to a friend. I expected them to sing “Happy Birthday” and blow out pretend candles. Instead, Evie announced: “I’ll be Tony Blair and you can be John Major.”

Most parents try to pass on their passions to their children - and are proud when the process works. A country-loving friend was just as thrilled when his little boy correctly distinguished between an occupied rabbit-hole and a disused one. But this is more than a matter of parental pride - the point is that pre-school and infant children can grasp far more about “adult” politics than we often imagine.

I talk a lot to Evie (now five) and her three-year-old sister, Rosa, about politics, current affairs and interesting stories I spot in the papers. As a political journalist, I like to share a little bit of my world with them, to help them understand why I spend so much time reading what Rosa calls “horrid old newspapers”. And, when the last election campaign was on, and my life was turned upside down, I wanted to include them in the conversations adults around them were having.

As term-time coincided with the last three weeks of the campaign, Evie had to come with me to the 8.30am Labour press conference. I drop her at school at 9.10am, just around the corner from Labour’s Millbank headquarters, but a long way from home. Taking her with me was the easiest way to get her there.

But she also found the experience fascinating, even if much of the talk went over her head. Her first exclamation on seeing the rows of hacks was, “Gosh, Mummy, I didn’t know boys could be journalists, too.” She was admirably quiet during the proceedings but asked scores of questions before and afterwards. What is the single currency? Why does it matter? Why are politicians so horrible about each other? Why do they always argue?

Such questions are not always easy to answer. I just about managed to explain the single currency, although I lost her somewhere between variable interest rates and depreciation. But as to why politicians argue, without the competing ideologies of socialism and capitalism, it is hard to explain the ritual abuse of Prime Minister’s question time or election campaigns.

Evie was desperate to ask a question at the press conference. She had worked one out for herself: “What difference will it make to me if Labour wins the election?” Chancellor-to-be Gordon Brown did call her, but mistook her obedient waiting for the microphone for shyness and moved on to someone else. Evie was mortified and, after a private intervention from me, a promise was made that she would have a chance again before the end of the campaign. This never materialised, and Evie has not forgotten. “You must mention the broken promise,” she said when I told her I was writing this piece.

What surprised her was how little interest in politics she found at her school, a Church of England primary in Westminster. The election was mentioned only once - the day before at assembly - and only because the school was to be used as a polling station. She told her classmates about the press conferences, but none asked her a question.

Evie’s biggest regret about the election, she says now, is that she had no vote. (She would have used it to support Labour, despite the broken promise. ) We took both the girls with us on polling day so they could see how the process worked. Rosa was lucky enough to have a mock election at her nursery school. Staff arranged for a representative from each party to talk to the children for a few minutes. Rosa voted Liberal Democrat but could not tell me why - only that they seemed “the goodest”.

Even at this age, children can be capable of grappling with political problems. When the Conservatives lost the Wirral South by-election earlier this year, and I explained to the girls this was good news for Labour, Evie said it must be very bad for John Major. “What was he going to do about it?” she asked. I turned the question around. “What do you think he should do?” “Blow up Parliament,” suggested the ever-anarchic Rosa. Evie thought a little longer. “Why doesn’t he pass a law saying everyone should vote Tory?” she asked. These are creative solutions, either of which John Major might have been tempted to use had he been able to.

It is not until children are made aware of the constraints under which politicians operate that they realise how difficult the business is. I had a long game with Evie the other day, in which she was pretending to be Tony Blair and I had to be John Major. We were trying to make schools better, but each time she suggested doing something that cost money, I asked: “Where will you get the money?” As the tax burden rose, she was forced to think more laterally. For example, to make boys work harder at school, she suggested having more tables in classrooms so “rough” boys could be separated from each other and surrounded with girls “to set them a good example”.

Of course, not all children will be this receptive. Whether the inheritance is genetic or environmental, I am lucky to have at least one child, possibly two, who shares my enthusiasm for politics. But many parents and teachers underestimate the ability of young children to understand and engage with the concepts that underlie the construction of the adult world.

After all, politics is a macrocosm of the world the child sees. Police stand in for parents, laws for family rules, taxes for parents’ income and spending on public services for family expenditure. Children know not everything can be afforded at home. They are intrigued by the parallel with a country. And they enjoy the idea that their apparently omnipotent parents have to abide by the rules others set for them - and can be punished if they don’t.

To a young child, the obvious solution must be to become the law-maker. Since Evie was four, her stated ambition has been to be prime minister. Her logic? “I really want to be a king, queen or princess. But I reckon prime minister is the closest I’ll get.” The good news is that at least she will have been in training from an early age.

Mary Ann Sieghart is assistant editor of The Times