It’s hard to imagine the scene below in Trafalgar Square, the way it may have looked 125,000 years ago.

Lion’s share of Trafalgar Square: this artist's impression captures what London's famous attraction may have looked like 125,000 years ago. Select images to enlarge.

And strange to visualise real lions, not stone ones, observing unsuspecting elephants and hippos grazing on the grassy banks of the River Thames. This unrecognisable landscape depicted above shows the river banks reaching as far east as Trafalgar Square, where cave lions, straight-tusked elephants, hippos and Stephanorhinus once roamed.

Large animals played a big part in London's past and there are surprising fossilised specimens to explore in our Britain: One Million Years of the Human Story exhibition.

Trafalgar Square today: The scene echoes the same lion’s lookout of the earlier picture, but it's a very different landscape. Below: a wilder picture of what's to come this weekend at the Square's Big Dance Live festival.

Fast forwarding to this weekend, much wilder scenes are predicted in the Square on Saturday, 12 July. The unsuspecting stone lions may be joined by as many as 5.3 million people grooving along to the sounds of London’s Big Dance Live festival (a previous event is pictured below).

Big Dance Live celebrations planned in Trafalgar Square on Saturday, 12 July.
© Foundation for Community Dance and the Greater London Authority

As recently as the 1950s, building work in Trafalgar Square unearthed evidence of London's wild past when a hippopotamus canine was found, dating back 125,000 years ago. It's displayed with other specimens and objects in our Britain exhibition against a huge pictorial backdrop of Trafalgar Square.

Trafalgar Square tooth: This hippo canine was excavated in the 1950s - on show in our Britain: One Million Years of the Human Story exhibition with other animal fossils from London.

The fossil evidence - much of which emerged in the late 19th century when major excavations took place in the city - shows that at different times, as far back as 400,000 years ago, animals such as hippos, mammoths, wild cats, bears, wolves, horses and elephants wandered freely throughout the area that London now occupies. All perfectly adapted to the changing conditions in the ice ages.

Hippopotamus and elephant remains beneath Trafalgar Square, woolly mammoth fossils down The Strand, woolly rhinoceros remnants under Battersea Power Station and reindeer fossils at South Kensingon Station: these are some of the significant London fossil finds our scientists are researching now.

Important discoveries like these will be highlighted at a special Day of Archaeology tomorrow, Friday, 11 July, which also marks the start of the two-week-long Archaeology Festival 2014. Museum human origin experts and palaeontologists including Professor Chris Stringer will join others around the country blogging on the day. Lots of festival events are planned for all ages throughout the week.

July events at the Museum feature a special Lates discussion with Chris Stringer and other speakers: tickets for Britain and Beyond also include entry to our Britain exhibition so get yours now.

• Britain: One Million Years of the Human Storry exhibition
• Britain events at the Museum
• Day of Archaeology
• Archaeology Festival 2014
• Trafalgar Square's Big Dance Live

She's 400,000 years old and her faceless skull is now mounted in an elegant display case in readiness for the Britain: One Million Years of the Human Story exhibition opening at the Museum on 13 February.

Could this 400,000-year-old skull, belonging to an early Neanderthal woman, be one of the first Neanderthals in Britain? The skull is one of more than 120 specimens and objects on show in the Britain: One Million Years of the Human Story exhibition.

The early Neanderthal woman's skull was found in Swanscombe, Kent and, despite its age, it reveals a great deal. Her brain left its mark on the surrounding bone. Faint impressions of folds and blood vessels show it was a similar size as a human's brain today.

The back of the Swanscombe skull has characteristic Neanderthal features, including a small pit where the neck muscles attached to the skull.

You'll see this striking specimen assembled as one exhibit in the exhibition, but look closely and you'll discover it actually comprises three parts.

Observing Museum curator, Rob Kruszynski, steadily hold the three skull pieces together at a recent photo shoot we attended, I listened intently as he recounted how remarkably well they fit together. Especially when you consider that they were found at different times in Swanscombe.

The central skull section (occipital) was found in June 1935 in Swanscombe, Kent, by a local dentist A. T. Marston. The left part (parietal) was found at Swanscombe in March 1936 also by Marston. And the right parietal was found years later in 1955, by archaeologists J. Wymer and A. Gibson. Select images to enlarge.

Being so close to this ancient woman's skull and watching Rob handle it so carefully, I found myself wondering who she was and what her life must have been like? Did she die alone or with her family around her? We don't know as much as we would like about Neanderthal lifestyles because nothing was written down, but we do know that they sometimes buried their dead, that it's likely they did have some form of communication and that they lived together in family groups.

This graphic reconstruction of a Neanderthal woman model appears in the exhibition. © PS Plailly/E Daynes/Science Photo Library

'There is analysis going on now on a large family group of possibly 12 Neanderthal individuals discovered in a cave site near to El Sidrón in Spain's Asturias,' Rob tells me. 'All had been cannibalised. And evidence suggests there were six adults (three males and one female), three adolescents between 12 and 15 years of age, two juveniles between five and nine years of age, and one infant, and that they were related.

'As of 2012, over 1,800 Neanderthal fossil remains and 400 tools have been recovered at El Sidrón, making it one of the largest collections of Neanderthal fossils in Europe to date.'

These El Sidrón finds are nowhere near as old as our Swanscombe skull, as they only date back to about 42,000 to 50,000 years, but they have been invaluable in revealing the Neanderthal's own story.

Our scientists and archaeologists continue to unravel more about our prehistoric ancestors with such amazing discoveries about the men, women, children, animals and objects they uncover and analyse.

• Visit the Britain: One Million Years of the Human Story exhibition to get the most complete picture to date
• Buy tickets to see the Britain: One Million Years of the Human Story exhibition
• Discover more about Neanderthals online