I'm walking through the echoing corridors of the University of Oxford carrying a Neanderthal skull swathed in bubble wrap.

A short distance ahead, the eminent zoologist Dr George McGavin is helping tote the torso of a skeleton. There's a bit of precarious manoeuvring going on as McGavin, assisted by our photographer, attempts to navigate the fragile bones through the university's Museum of Natural History.

It's not a real artefact, but a convincing model specially constructed for new BBC television series Prehistoric Autopsy. Even so, given what the props department have told us about insurance, it's not something you would want to drop. Eventually, after four flights of stairs and several anxious moments, the model – based on the Neanderthal La Ferrassie 1 whose bones were found in a French cave in 1909 – is in situ in the cavernous Huxley Room.

This space, housing one of the world's largest insect collections including some of Charles Darwin's specimens, is where McGavin spent much of his tenure as assistant curator of entomology at the museum. The Glasgow-born zoologist has become a familiar face on our television screens, fronting BBC's popular Expedition series as well as documentary The Dark, about the nocturnal activities of animals, and After Life on the science of decay.

In battered-looking jeans, his blue denim shirt haphazardly rolled up at the sleeves and a snazzy messenger bag over his shoulder, McGavin is the antithesis of the crusty scholar. He has the trademark academic beard, it's true, but there's a mischievous twinkle in his eyes as he ruffles his thick grey hair to make it stand on end.

As the go-to guy of the insect world (he's a resident expert on The One Show and once appeared on Richard & Judy demonstrating how to cook creepy crawlies), McGavin, 58, is now turning his hand to a new challenge. Over three evenings this week, he and leading anatomist Professor Alice Roberts will consider what life was like for three now-extinct human species: Neanderthal, Homo Erectus and Australopithecus Afarensis, aka "Lucy". In each episode, their findings will help a paleoartist decide how to reconstruct an entire body – from the bones up – to be unveiled in a tah-da moment at the end.

The glossy series, filmed at Glasgow University and made by BBC Scotland, will attempt to decode the day-to-day existence of the chap we have now left upstairs, La Ferrassie 1, and his peers.

"My role," explains McGavin, "is to ask the experts questions that the viewers want to know. So if they hold up a bone and say: 'From this I can tell blah-de-blah' I say: 'Really? Explain that to me. How can you be sure from the angle that the animal walked upright?'"

The opening programme challenges some of our most common perceptions about Neanderthals, not least that these were lumbering, knuckle-dragging beasts. "They were certainly heavily built," concedes McGavin. "They had to be. But we are becoming more aware that they were not the brute thugs that we thought they were. They obviously had culture of some sort, they were very smart. They may even have had art.

"What we are trying to do is extrapolate from a few bits of bone – we haven't any flesh, organs or tissues – what these beings were doing, how they lived and behaved."

In the series, both McGavin and Roberts have their DNA analysed by experts as part of an attempt to determine how much Neanderthal humans possess within their genetic make-up. One question McGavin doesn't fight shy of is whether the two species interbreed. "Did Homo neanderthalensis and Homo sapiens have sex?" he wonders aloud. "That could explain why we possess a certain fraction of our genes which are Neanderthal. Some scientists say yes, some say no.

"It's very hard to get direct evidence, but if you assume the sexual habits of hominids haven't changed a huge amount, there are males today who will have sex with just about anything. It's an aberration, but it happens.

"I would find it improbable that a Neanderthal male, upon finding a Homo sapiens girl, would not have a crack at it, to put it in crude terms. Some individuals in the field say it's pretty clear that hybridisation took place – they had sex. Others say no, you could get that percentage of genes inside your genome because we share a common ancestor and so we always had those."

What does McGavin believe? "All I'm saying is I wouldn't be at all surprised if a Cro-Magnon [early Homo sapiens] girl was molested by a Neanderthal because we shared the same areas for 35,000 years, which is a long time."

The show also addresses the contentious issue of cannibalism. "There is evidence on bones that flesh was hacked off, meat cooked and so on," he says. "Some scientists say that is clear evidence that Neanderthals were prone to eating each other. Again, I don't see any evidence as to why that oughtn't to have happened. You don't have to go that far back in our own history, perhaps only 100 years, to find humans in areas of the world who did eat each other."

Some scientists refute the theory, interpreting the bone marks as evidence of animals walking over the remains, or simply wear and tear.

Why are we humans so fascinated by our history and roots? "They're questions we have always asked: where did we come from and how did we arrive here?" says McGavin. "I'm sure some viewers will think it's absolute hooey and that God made everything in six days. It's a great story – but we have moved on from that." Across the world, he says, "hominids" have always tried to make sense of the world through creation myths. But those are fanciful tales: "It's not factual; it's not science."

Born in Glasgow, McGavin moved to Edinburgh with his family aged five, and attended the prestigious Daniel Stewart's College. His late parents, George and Margaret, were respected artists. His elder brother would go on to become head of a university English department; his twin sister an advocate. McGavin describes himself as a shy, awkward child with a bad stammer, who would lose himself in the world of nature.

"Plants and animals fascinated me," he says. "My stammer got worse and worse. By the time I was 14 it was off the scale. If you had said to me: 'You are going to be a university lecturer for 30 years and then become a television presenter,' I couldn't have imagined anything more absurd. I was average at school in everything apart from biology – in that I got every prize going."

He loved reading, and spent hours in Edinburgh's Blackhall Library, poring over text books and becoming annoyed when librarians informed him that the Encyclopaedia Britannica was for reference only, and he couldn't take it home. When he didn't have his nose in a book McGavin could be found scouring the countryside for interesting specimens. On holiday with the family on Scotland's west coast he would devise projects for himself, such as studying rock pools, pressing flowers or collecting bird skulls, though this last had to be curtailed "otherwise you fall foul of the mum asking: 'What is this disgusting, decaying bird's head in the fridge?'"

He studied Zoology at the University of Edinburgh before completing a doctorate at the British Museum of Natural History and Imperial College, London. He spent 25 years at the University of Oxford as a lecturer and assistant curator of entomology at the Museum of Natural History, and is currently an honorary research associate at the museum.

It was as a student in Edinburgh, however, that his passion for insects was kindled. "In my second year we went on a field trip and all my class were into badgers, owls and large creatures, yet at our feet were countless millions of ants. I realised: 'These are equally interesting, they are right here and we can observe them'."

Did I know that 66% of all species are insects? And that animals with backbones, such as fish, birds, bats, cats, rats, dogs and humans, account for a mere 2.8% of all species? "The real engine of the Earth," says McGavin, "is small organisms: bacteria, fungi and insects. You could remove all the big animals off the face of the Earth tomorrow and it wouldn't change depreciatingly, but if you took away the bees and ants the place would fall apart in a short period of time."

Several insect species have been named in McGavin's honour. What are they called? "Uuuurgh," he groans, "they all end in M-C-G-A-V-I-N–I. But I can't remember what they all are. There is a cockroach, a plant hopper, an ant, a shield bug and something else." He gives a nonchalant shrug.

Five years ago, McGavin had an epiphany as he was driving home after a long day of tutorials. "I had the dream career, it was perfect, I couldn't have written a better job spec," he recalls. "I did research, teaching, lectures, field courses and travelled. But yet, I wasn't fully happy.

"I had this realisation that if I did a tutorial I might have an audience of four, if I did a cruise ship talk it might be 400 but if I did an hour on telly I would have four million." He resigned the following day. "I knew some people would be horrified I'd given up a tenure to go into what they might see as the fickle world of TV," he says. "My life, though, has been about education. It's about sharing my passion for the natural world with anyone who cares to hear it. I used to interview potential students for Oxford places and I would often ask the kids about their early influences. Eight out of 10 would say: 'Attenborough'. So, television is important."

These days McGavin lives on the outskirts of Oxford with his wife Lois, a retired probation service officer. Their 25-year-old daughter, Amy, is an actor, his stepdaughter, Alice, 34, PA to a company director. He's kept busy, with no fewer than five programmes currently in production, including three-part shows Swarm Chaser and Planet Primate, a 90-minute BBC Four special, Ant World, and a documentary, Miniature Britain, designed to encourage us to "look at the small things on Earth".

"Everyone wanders around, looking for the blackbirds and owls," he says, "but the interesting stuff is the things you can barely see. If I had a load of money I would buy a hand lens for every child aged under age of 10, so they could look at insects, bark and flowers. Instead, folk give them Game Boys and iPods."

As for Prehistoric Autopsy, the programme will reveal how much we share with Neanderthals – something McGavin reckons might surprise a lot of people. "We are very similar indeed," he says. "Homo neanderthalensis is definitely very, very close to us." He chuckles. "One day, who knows, perhaps as the ice sheet recedes, we may find a frozen part of a Neanderthal. That would be bloody amazing."

His biggest hope, though, is to turn on a new batch of minds to the wonders of nature. All this talk of dumbing down at the BBC is nonsense, he says. "If you just had a programme with masses of facts, people would get bored. You have got to make it exciting, snake the facts in so they are almost unaware of it.

"You have to fire them up. Anyone who says otherwise is an eejit."

Prehistoric Autopsy will be shown on BBC Two, Monday to Wednesday at 9pm. The accompanying tour will come to the National Museum of Scotland, Edinburgh, from November 23-25. Visit www.bbc.co.uk/prehistoricautopsy.