The Ship BBC2, From August 20, 9pm

“She’ll go wherever there are open arms - she makes friends all over the world.” That’s what one person close to her has to say about the Endeavour, the replica of the ship in which Captain James Cook made the first of his epic voyages of exploration, from 1768 to 1771. Built by a group of Australian enthusiasts, this Endeavour has been travelling the world’s oceans since 1994: this month, after seven weeks’ anchorage in Whitby, Cook’s birthplace, she is about to go “on exhibition” in Boston, Lincolnshire, before visiting London, Southampton and other ports later this year.

Endeavour is likely to attract more friends - or at least curious visitors - than ever in the coming weeks, as she is at the centre of a new BBC2 series, The Ship, a six-parter in which some 50 volunteers - including specialist historians, a botanist and other experts - recreate one leg of Cook’s voyages, from the east coast of Australia to Java. Yes, it’s another manifestation of that apparently popular television genre, the history-as-relived-by-willing-volunteers series (recent instances: The Trench, The Edwardian Country House, Surviving the Iron Age). But this is different, insists Chris Terrill, The Ship’s director-cameraman.

“I have problems with programmes where people are transformed into First World War soldiers or whatever - it’s silly and rather uninformative. I think you have to say: I am what I am, I’m a 21st-century person; but I am following in the footsteps of these historical characters, trying to get a greater understanding of what they achieved.”

In search of this understanding, the BBC team went to some trouble. Retired RAF pilot John Jeffrey, now a freelance sailing instructor, was one of the volunteers who plotted the Endeavour’s course for the voyage using only techniques known to Cook (at other times, the ship’s professional crew use up-to-date navigational aids.) This meant learning 18th-century techniques to establish the time (and therefore longitude) at sea. Because the lunar-distance method of Cook’s day had to be used, and modern methods of calculation were outlawed, the team had to have special tables drawn up - “tables that said if the sun and moon are this far apart, then this is the time now,” says Jeffrey - just as the then Astronomer Royal, Nevil Maskelyne, had provided tables for Cook’s voyage.

The other problem was having to use “the sort of charts Cook would have had available to him. They were rubbish - French copies of something that a Dutchman had told a Portuguese, that sort of thing. It’s no use whatsoever to get your position precisely if you’ve got a chart where the longitude is wrong. But at least we had the advantage of knowing that Cook had succeeded. He is my hero, no doubt about that.”

There were other deviations from Cook’s practices. For a start, there were women on board, and the crew came from a wide variety of backgrounds. “But we gelled incredibly well,” says ship’s doctor Claire Edwards, an orthopaedic surgeon from Nottingham. “There was the odd person who wasn’t keen on doing maintenance. To keep an 18th-century ship sailing she has to be looked after, which means two hours every day sanding, varnishing, oiling and tarring. But in such a tight community you can’t really have bad sentiment brewing. Any problems have to be sorted or forgotten about.”

Chris Terrill also chose to have “representative” Aboriginal and Maori crew members, “which Cook would not have had, of course. For them, the Endeavour is a symbol of colonisation, it’s got a very different resonance.”

In the first episode of The Ship we see a protest against the expedition by a boat flying the Australian Aboriginal flag. “At first I thought, ‘Oh no, this is all we need’,” recalls Terrill. “Then I realised it was a piece of good fortune, a perfect indicator of the legacy of history. I was very keen to look at the way history illuminates the present and what it means for modern Australians. It helped us all to appreciate that history can be taught many ways.”

Teaching history isn’t quite Terrill’s job, but before he joined the BBC 15 years ago he was a teacher: in the 1980s he was head of geography at Rendcomb College in Gloucestershire, having previously acquired a degree in anthropology at Durham University and spent five years in Africa. “I still regard myself as an anthropologist,” he says. “I just happen to be doing it with a camera.” Certainly some of his previous BBC series have had an anthropological feel: Through the Eyes of the Old or Soho Stories, for instance, or even the award-winning “docu-soap”, The Cruise.

The Ship is, however, his first venture into the past. “The BBC history department asked me to come in as an observational film-maker, and put the history in the context of a modern adventure.” He still regards himself as an educator (“I’ve just got a slightly larger class than I used to have”), and gives talks to schools, “either about film-making or about specific adventures I have had. You might have a big audience for television films but you can’t see them. They can’t put their hands up and ask questions. I miss that.”

He also misses the Endeavour. “I think a lot of us would have liked to carry on. But it’s difficult to get 56 people together and say ‘Right, cancel your life for six weeks’. Cook went off for three years not knowing when he’d be back. We have mortgages and bills and family to worry about - another reason why we couldn’t become 18th-century people.”

‘The Ship: in the wake of Captain Cook’, BBC2, Tuesdays, 9pm, from August 20. Support material on www.bbc.co.ukhistory. ‘HM Bark Endeavour’ is at Boston, Lincolnshire, August 17-26; Thames Quay, London, August 31-September 8; Southampton Boat Show, September 13-22; various other ports through the autumn. Open daily 9am-7pm; admission pound;7 adults, pound;4 children; family ticket (up to five people) pound;18; school groups pound;3 per pupil, one free teacher’s place per 15 pupils. Group bookings and tour details on 01723 232587; email endeavour@whitby.net. The official ‘Endeavour’ website is at www.barkendeavour.com.au.