My walks to the British Museum as a young boy must have been as much a visual and emotional education as they were an untiring thrill. The time I spent there as a child is probably one of the reasons I came to travel so much to remote spots and folds of the atlas in later years.

The museum itself is a map of the world, a time machine, too, offering mind trips to Mesopotamia, Memphis, Athens in the golden age of Pericles and to an encyclopedia of compelling civilisations, or haunting fragments of them. Here, dreams of exotic places, peoples and buildings were brought to kaleidoscopic, three-dimensional and mesmerising life.

I liked, too, and lapped up, the way in which the tight, regular grid of what remained of Georgian Bloomsbury – streets animated by uniform parades of red double-decker buses and ranks of gleaming black cabs – gave way, all of a sudden, to an enormous courtyard set behind glossy black iron railings.

Beyond – up the most generous flight of steps – lay the museum itself, and its compelling collections veiled by a great Greek Revival pediment at the centre of an ambitious colonnade of no fewer than 44 Ionic columns, their design based, as I learned much later, on those of the Temple of Athena Polias at Priene in Asia Minor (now western Turkey).

There was all this to take in even before walking through the doors into the echoing lobby and deciding whether to turn left – into the dark realm of Egyptian mummies and Assyrian gateways guarded by warriors who were half adventurously bearded men and half vigorous blue ceramic bulls – or right into the Corinthian light of the King's Library, with its double-deck rows of gold-embossed leather spines.

Here I could stare at the pencilled pages of Scott's Diary, not knowing that one day I would hold this most moving of documents in my own, white-gloved, hands, turning its heart-rending pages.

I enjoyed the gloom of the Duveen Gallery, built just before the second world war to designs by the American architect John Russell Pope, where the Elgin Marbles – the Parthenon frieze – were on display. I was ignorant then of the controversy around these "stolen" sculptures and the desire of many modern Greeks to see them returned.

I learned to love Sydney Smirke's circular Reading Room set under an iron-ribbed dome in a courtyard of his elder brother's Grecian pantechnicon. Robert Smirke had travelled extensively in Greece and Sicily to sketch the ruins of ancient temples before he turned his cool mind and his elegant hand to the design of what is today, in terms of visitor numbers, Britain's most popular tourist attraction.

What has changed since I was a child? Renovations, extensions, and the exodus of the British Library to Colin St John Wilson's red-brick monument alongside the fairytale Gothic of the Midland Grand Hotel and St Pancras station, Norman Foster's roofed-over Great Court and, most of all, the sheer number of people tramping through the museum's halls and galleries, so many that the last time I came to look at collections from ancient Mesopotamia I was all but swept away on a tide of visitors: the gallery I had chosen has become one of many intensely busy thoroughfares in the museum.

It can be too busy for its own good. And yet anyone who is tired of the British Museum is tired not just of tourism or the crush of central London, but of the entire world and the history of its civilisations captured here in untiring architectural splendour.

• Admission to the British Museum, Great Russell Street, WC1 (020-7323 8299, britishmuseum.org) is free