Amanda, who was pregnant with a little boy

As a photographer, Jemma Watts loves to travel. She has always said that if she had a little girl she would call her India, because of her love for the country.

Yet it’s another country that she plans to make special for her child. When she shows him or her the world, she will make an extra effort to visit Denmark regularly.

‘I’ve spent a long time thinking of how we would travel to Denmark, go on holiday there, learn about the history and the culture,’ she says.

That’s because she is planning to have a Viking baby, raised in Britain, but proud to be half-Danish. Ideally, she would love to have a couple of babies — she jokes about the prospect of Viking hordes.

Her vision of the future is vivid, but poignant, because Jemma isn’t pregnant and does not have a partner. She is one of the thousands of British women who are pinning their hopes on having a Viking baby, thanks to Danish sperm banks.

Jemma, 41, is one of the women followed in an extraordinary BBC documentary that goes behind the scenes at several clinics, including Cryos in Aarhus, the biggest sperm bank in the world.

Every year, hundreds of women like Jemma travel to Denmark for treatment or, more commonly, buy Danish sperm over the internet to be used in British clinics or at home via self-insemination.

Some are women whose partners have fertility issues, but the majority are lesbians or — and this is the fastest-growing type of client — single women in their 30s and 40s who do not see why a lack of partner should be a barrier to motherhood.

As documentary maker Sue Bourne puts it: ‘The Danes are famous for exporting beer, bacon, Lego — and now sperm. I don’t think most people have any idea of the scale of what is happening because the women who do it tend to be secretive.’

A Viking baby doesn’t come cheap. Danish sperm bought over the internet and delivered to an address in Britain costs £460.

If a woman travels to Denmark for clinical insemination or further fertility help, the price soars to several thousand pounds. Factor in the cost of travel and accommodation — and that several trips may be needed (six or more is not uncommon) — and it can be extremely expensive. One woman has spent £75,000 ‘and stopped counting after that’. Yet the Cryos clinic (motto: ‘Congratulations, it’s a Viking’) has been running for 25 years and boasts 30,000 babies born worldwide. It is only in the past few years that there has been a ‘Viking invasion’ of Britain, due to changes in the law that banned anonymous sperm donation in Britain, leading to a rapid decline in donors.

A British sperm donor has to be prepared for the fact that any resulting child will have the right to trace them at the age of 18.

Made in Demark: One woman already raising a Viking baby is British journalist Jessica McCallin, who was in her mid-30s when she conceived her daughter Freya, now three

But the idea that British women turn to Danish donors because it offers an anonymous solution is way off the mark.

Many reject the anonymous option and seek ‘open’ donors: Danish men happy to be contacted by any resulting offspring.

As the law stands, if British women are being treated through a clinic in Britain but using Danish sperm, they only have the option of traceable donors. But even some of those going it alone choose open donors.

So how easy is it to buy Danish sperm? ‘It’s as easy as shopping on Amazon,’ says Kel Cooke, 33, who is in a civil partnership with her partner Anna.

‘I remember saying to Kel just after we met: “I know I am going to have your baby,” ’ says Anna. ‘I didn’t even know then how that would be possible. But it is.’

The pair are filmed shopping for the biological father of their future child. The transactional nature of their quest is eye-watering, as is the ease with which a father can be cut out of the equation.

‘It’s easier than adopting a puppy,’ says Kel.

The detail given about a Danish sperm donor is extensive, which is part of the attraction.

The Danes are famous for exporting beer, bacon, Lego — and now sperm Documentary maker Sue Bourne

With a British sperm donor, you get a number and choice of hair colour. ‘This man is British, white and has brown hair. That’s basically it. You take pot luck,’ says Kel.

‘With a Danish sperm bank, you get every detail you can imagine: family background, job description, education and pictures of the man as a baby or child.

‘Donors write personal messages about why they are a donor. You even get to hear their voice.’

Kel and Anna spend hours going through profiles on the clinic’s website. The donor they choose writes movingly about how he would like to have had a wife and children, but it has not happened because he is a farmer ‘and not everyone wants to be a farmer’s wife’.

He is keen to be a father, even of children he may never know, because, he writes in faltering English: ‘Who will remember me in 100 years if I no children have.’

Kel and Anna tap in their credit card details and a few days after this rather cold transaction is completed, the sperm donation is delivered to their door.

Jemma spent weeks poring over the Cryos website, fretting about her decision.

‘For me, it was like a dating site. I picked the man who came closest to the one I would want to be the father of my child in real life.’

She made her final selection based on a report from the Danish clinic staff who had met her donor.

‘They gave him a glowing reference, saying they couldn’t recommend him enough. They said he was always happy and joking when he visited the clinic.’

One woman already raising a Viking baby is British journalist Jessica McCallin, who was in her mid-30s when she conceived her daughter Freya, now three, using Danish donor sperm. Single and unwilling to settle for ‘Mr Good Enough’, she wanted the donor to be anonymous, which is no longer possible in Britain.

‘I gave the anonymity issue a lot of thought and ultimately came down on the side that it would be better for my child,’ she says.

It’s as easy as shopping on Amazon Kel Cook

‘I felt that if I’d made this decision to use a sperm donor it meant the biological father wasn’t going to be in their life and it was simpler to take him out of the picture.

‘I am often mistaken for being of Scandinavian descent. I’d done research, which suggested it helped if donor children look as much like their family as possible, so that was another tick in the box.’

The five women who were followed in the TV show include Holly, 36, who is lesbian and single, and jets back and forward to Denmark each month to be treated, and Amanda, who was pregnant with a little boy at the time of filming.

She’s the only one who knew motherhood was imminent when the cameras started rolling. We have agreed not to reveal before the documentary is broadcast whether the other women were successful in their treatment.

All talk of the emotional toll the process took. The overwhelming feeling is this is no easy option.

‘Some women went through the process ten or 20 times at huge expense,’ says Sue.

The participants were given cameras to film the selection process, the clinical aspect and the all-important pregnancy tests.

Jemma had reservations about showing her fight to be a mum publicly, but felt it was important.

‘This isn’t talked about, but there are thousands of us out there doing this. It is the loneliest thing in the world to go through on your own,’ she says.

For while these women appear to be ready to be single mothers, the lack of support of a partner is painfully obvious.

You might describe Jemma as a typical career woman who left it too long to have a baby by traditional means, but she is offended at that.

The BBC documentary went behind the scenes at several clinics, including Cryos in Aarhus, the biggest sperm bank in the world

‘My brother said it about me, but that’s just not the case. I thought I would be married by 24, with babies at 26. I wanted at least three — two girls and a boy.’

She had relationships, but ‘not the big one where you think: “This is it — I want to have babies with this man.” I wasn’t prepared to settle’.

At 38, she started to worry about when she was going to be able to start a family and, with no sign of a life partner, decided to freeze her eggs. However, she was devastated by the result of medical tests.

‘They said my eggs weren’t worth freezing. I’d left it too late. At best, I was told, I had another year of fertility left,’ she says.

‘I came out in absolute bits, then I decided to go it alone. I hadn’t given up on men, far from it, but I decided I had to have the baby first, then hope the husband followed.’

There are ‘easy’ ways for a single woman to get pregnant — as she was told by friends.

‘I was told “Go and have a one-night stand”, but I didn’t want to have a baby like that. How would I explain that to my child? And it’s not fair to trap a man.’

People do not always tell us when they have babies, but we estimate there are between 3,000 and 5,000 of our Viking babies in Britain Cryos director Ole Schou

Not everyone understood her decision to opt for a sperm bank. ‘Some people told me I was being selfish,’ she says. ‘That hurt. Someone said “Why not adopt?”, but single mothers are bottom of the pile when it comes to adoption. You are likely to get a child who has been abused or has problems.

‘Besides, I wanted my own child. Is that so awful?’

The curious thing about Jemma is that she continued to hope for a ‘normal, traditional family life’ while making arrangements with the sperm bank.

She goes on a date right after injecting herself with fertility drugs — and agonises about telling the unsuspecting man.

‘Of course I couldn’t,’ she says. ‘You can’t exactly say: “Oh, I’m being inseminated next week.” ’

Kel and Anna ended up being more open about the insemination attempts than they had intended.

‘Babies aren’t normally conceived in a clinical setting,’ says Kel. ‘We wanted candles, soft lights.’

That is scuppered by the fact the sperm is delivered in a large yellow canister that looks like a Tardis and the untimely arrival of Anna’s parents.

‘My parents rarely leave their home village, but they picked this one day of the year — when I was ovulating and the chart said: “Go! Go! Go!” — to visit,’ says Anna. ‘So we had to tell them.’

While her parents had no problems with their daughter’s sexuality or her wedding to Kel in 2010, they had not thought children were part of the equation.

‘They were stunned, but I am so proud of how they dealt with it. I thought they would have trouble getting their heads around the science or the ethics, but they just went straight to the idea of having grandchildren.’

Cryos director Ole Schou believes there are between 500 and 1,000 Danish babies in the UK from his clinic alone

Yet the film does raise difficult questions. Asked about his responsibilities to a possible future child, one donor says he would be happy to have a coffee with them when they reach 18. He would, he says, even go so far as to buy the coffee.

Some will undoubtedly be horrified at what these women are doing and there are huge issues around monitoring the number of times each donor can provide sperm.

There are few controls, ‘meaning one donor can potentially have hundreds of babies’, says Sue. It raises the question of whether babies from the same donor could end up meeting unwittingly.

Even though it’s impossible to say how many babies in Britain are born each year as a result of Danish sperm donations, Cryos director Ole Schou believes the figure to be between 500 and 1,000 babies from his clinic alone — this figure has ‘increased dramatically’ in the past few years.

‘People do not always tell us when they have babies, but we estimate there are between 3,000 and 5,000 of our Viking babies in Britain.’

The Viking invasion certainly shows no sign of slowing. Cryos, like other sperm banks in Denmark, has specialist staff who deal with British clients, and there are clinics in Denmark affiliated to British ones.

One less quoted statistic, however, is that 75 per cent of fertility treatments fail.

‘That is why so many people who want to have babies go on and on and on trying,’ says Sue. ‘Once they have opened up the floodgates of wanting a baby, it’s not something you just shut down again.’