Horniman Museum Forest Hill, London

My 95-year-old aunt still remembers taking her little brothers (my father included) to the Horniman Museum during the First World War. Seventy years later, my wife and I took our children on wet Sundays, while I brought my Peckham primary classes for weekday visits.

The Horniman is one of the best destinations in south London, created 100 years ago by the tea merchant Frederick Horniman on the summit of Forest Hill. A true representative of philanthropic Victorian values, he dedicated the museum to “the people of London forever, as a free museum for their recreation, instruction and enjoyment”.

It’s always been a place for families. Whenever you visit, parents and grandparents from around the world are showing the rising generations things they knew when they were small. When I went to see how the museum has changed with the recent opening of its pound;13 million extension, I bumped into Claudia Bennett and her four children. Claudia’s home is now in Atlanta, Georgia, but she grew up nearby and loves to return to a place filled with happy memories. She and eight-year-old Felicia said the old and the new worked their magic.

The new is certainly impressive. The building has, in effect, been rotated through 90 degrees, so now it opens directly on to the 16 acres of Horniman Gardens, just as its founder wished. Visitors can marvel at some of the best views in London, or picnic in a beautifully maintained flowery landscape; or they can, as of old, climb the stairs from the bus stop up to the doorway of one of the most striking Art Nouveau buildings in Britain. Once inside, you find yourself at the Central Square, one side of which looks out at Horniman’s own superbly restored conservatory. From this hub the white walls of the new galleries tempt you onwards.

What they contain justifies David Attenborough’s enthusiastic affirmation that here we have “a universal museum”. The accumulated 250,000 natural history specimens, 80,000 ethnographical items and 8,000 musical instruments can’t all be exhibited at once, but there is more than enough on show to excite wonder, pleasure, puzzlement and laughter. The Centenary Gallery celebrates the institution’s own history. Showing examples of its whole range under varied lighting, it does much more than make you gasp; the discerning viewer begins to notice how objects have taken on changing significances, according to the acquisitive or classificatory principles of their collectors. Anthropological and social theory is on display in a most stimulating and comprehensible manner.

The African Worlds gallery is even more vibrant. You can get close to an Egyptian mummy or to a set of Benin bronzes, with none of the sense - sometimes felt in the British Museum - that your own interest is stifled by the sheer quantitative weight of what you see. And there is usually a child here, gazing at the Nigerian ijele. This 20ft high ceremonial mask is the only one in Britain. Covered in human figures, mirrors, feathers and symbolic patterns, it compels even the youngest or most casual observer to think about colour and design, shape and purpose, history and culture. Any class would be inspired to devise new works of art of their own.

The Horniman houses the best musical instrument collection in Britain. The new Music Gallery, which opens in October, uses the latest technology to become even more accessible. There are sections showing how music is used throughout the world for ritual, entertainment and celebration; videos light up the glass wall of a cabinet, demonstrating how the instruments within are played and what they sound like. “Sound showers” enable you to stand in a specific spot to listen, while visitors a few feet away are undisturbed. Interactive panels let you choose from hundreds of other instruments and play with them at the touch of a button.

Old favourites are still there. The torture chair from the Spanish Inquisition, one of Horniman’s first purchases, continues to evoke a frisson of righteous horror, though the museum is prepared to admit that its authenticity might be a doubtful. The Mexican dance masks still look out with bulging eyes above their luxurious moustaches, and the sea horses still gambol in their tanks. Best of all, the vast walrus remains as an emblem of the taxidermist’s art. Hundreds of thousands of children have met its frozen melancholy gaze, just as countless adults have thought how much it resembles a backbench Tory MP of the old school.

You can’t stroke the walrus, but there’s plenty for hands to do. The centre of the museum’s education policy is to develop unmediated connections between visitors and objects. Perhaps the most exciting innovation of all is the Hands On Base, where almost 4,000 pieces from the collection can be felt, caressed, squeezed, shaken, sniffed, rubbed or tickled. Carolyn Roberts, the head of education, wants visitors to make the museum a direct part of their experience by selecting and juxtaposing items, thereby curating their own mini-exhibitions. “By exploring pathways through the objects, by discussing how to group and classify them, visitors can bring their own understanding to bear on what they see and hear and feel,” she says.

The sprawling sculptured lion in the Africa Gallery roars out to be stroked. Rather than forbid this, as other museums might, a notice says:

“Please touch the lion gently.” The Horniman Museum is like that. It acknowledges that its visitors are human beings, curious creatures always capable of excitement, awe, sympathy and delight.

The Horniman Museum, 100 London Road, London SE23 3PQ. Trains from London Bridge, Victoria, East Croydon. Free, daily 10.30am-5.30pm. For details of holiday events for children and families and term-time education programme, tel: 020 8699 1872; fax: 020 8291 5506; email: schools@horniman.ac.uk or communityed@horniman.ac.uk; www.horniman.ac.uk