Alison Boulton digs beneath the city's dreaming spires

A while back, I went for a walk on New Year’s Day with my family, friends and cousins. We strolled through newly opened footpaths in Cornbury Park, Charlbury, and stopped at a crossroads when we reached a tree with a rope swing.

Hanging upside down, children running around all over the place, I was aware of another small party of walkers approaching: two parents, three children, an older lady and one or two darkly dressed men at the rear, one holding a child’s hand. A tall man had a baby in a frame on his back.

He stopped to consult a map. We called them over to try out the swing. The man carrying the baby called out, politely: “No thanks, another time maybe.” It was David Cameron, with Sam and their children. As they walked on, the rope broke. Just as well the PM was not swinging from it at that moment.

Yet the easy domesticity of the scene, the small party of close family was striking. The Camerons were doing what we were doing: enjoying the Bank Holiday with family and friends. He wasn’t at Chequers, or on a billionaire’s yacht. He wasn’t at Downing Street, unable to leave his papers. He’d chosen the New Year holiday to be close to his constituency home in the hamlet of Dean.

Good to know, too, that Special Branch do childcare when needed.

Later, we passed David Cameron again. This time, he was standing with his hands on his hips, while his two older children toughed one another up, rolling on the ground. He stood back – apparently not knowing how best to intervene.

Again, I felt the ordinariness of the scene, and a keen solidarity as a fellow parent. We’d all been there.

The celebrated political biographer Anthony Seldon, speaking in Oxford recently asserted that David Cameron “absolutely loved” being Prime Minister.

Yet the challenges the role of First Lord of the Treasury presents have never been greater, especially to the parents of a young family. As Prime Ministers have been elected younger, so their remit has changed. Anyone who has raised a young family knows how demanding it is in terms of time, effort and patience. Children take as much time as you’re prepared to give, and more. You side-line your partner one moment, put on them the next. Add a job which entails long, unpredictable hours, living over the shop, press scrutiny, much reduced privacy and constant access from officials and it’s a wonder anyone can successfully combine the two.

Yet seeing David Cameron that day, in easy informality with those closest to him, made me realise that prioritising a private life can be successfully achieved, even in office, before the next crisis breaks.