The number of sperm donors is apparently dwindling since new rules were introduced allowing offspring to trace their biological parents.
By Jane Dreaper
BBC News health correspondent
But behind the lifting of anonymity lie some happy endings too. The BBC's health correspondent, Jane Dreaper, talks to those involved in a project to introduce sperm donors and donor children.
Reports say the UK is suffering from a shortage of sperm donors
It is a beautiful summer's day on the terrace of one of London's top restaurants.
Will Calder is a thoughtful 41-year-old man. He usually chooses this venue for confidential business meetings.
But today he is here to tell me about his history as a sperm donor.
"The hardest thing was starting it - it was actually extremely difficult to go about becoming one," he said.
"It's not really in Yellow Pages. I actually rang up local hospitals and had the great pleasure of being put through to a variety of nurses who would shout across the ward - 'hey Doris there's somebody here who wants to be a sperm donor - what do I tell them?'
"Bear in mind I was a 17-year-old boy - you're embarrassed about these things in any case."
You might wonder why Will put himself through this excruciating experience. But he told me he had witnessed the pain of infertility experienced by some family friends.
And he admits that the £10 fee for each donation boosted his student grant.
"This was at a time pre-Aids," Will explained. "In those days donations were either used fresh and immediately to a recipient waiting in a waiting room round the corner, or were frozen.
"I was doing it for something like three or four years - one or two donations a week - so that's quite a number of donations over that period of time."
Some 18 years have now passed.
Because the young people he helped create are beginning to reach adulthood - and there could be many of them - Will has contacted the UK Donorlink project.
He probably will not go so far as meeting any of his offspring - because his partner has reservations - but he wants to help any young people who need information about their biological father.
"I'm sure it will happen - but if it doesn't that's OK. This is not about what I want out of the game."
It struck me that he must feel curious about the people whose lives were created as a result - especially as, unlike a parent who gives away a child for adoption, he has no idea about these offspring - even down to their gender and how many there might be.
"There is absolutely curiosity - I cannot deny that," Will told me. "Quite apart from anything else, I have an opportunity to see what my own two children may be like in eighteen years' time.
"But there's no element of possessiveness to this. It's simply a benign curiosity and a desire to do no harm - and even prevent harm and distress."
That sense of distress, isolation and even shame can feel very acute to donor-conceived people.
Experts equate it to the need that many adopted children have to know more about their origins.
For Louise Jameson, the Ugly Duckling fairytale by Hans Christian Anderson sums up how she felt.
Louise did not like her appearance when she was younger, and felt as though she never belonged.
During a rainy day on holiday, when Louise was aged in her early 30s, her mother broke the news that she'd been conceived with donor sperm.
"It was massive," said Louise. "All of a sudden who I thought I was, I wasn't. I cried a lot. It was just completely and utterly destabilising."
The years that followed were, in Louise's own words, complex and dark.
But she'd come to terms with the nature of her conception by the time she heard about UK Donorlink, which was set up on the cusp of a new era of openness.
"I had a deep conviction that it was simply not right to create people, to hold information about the origins of those people and withhold that information from them. It was basically immoral," added Louise.
Louise and her mother gave samples of cells from their cheeks to be sent away for DNA testing.
Out-of-the-blue, some months later, came a letter confirming she had been matched with other people in the project.
The information led her to the identity of her biological father.
"Even just having a name, having a face, having somebody solid - just that information, that knowledge - it just puts a concreteness into me," said Louise.
Although he's now dead, this was a prolific donor.
So far, Louise has met eight half-siblings -- they include other adults conceived from his donations, and all of them are new family.
One of them is Shirley. I caught up with Louise and Shirley over a cup of tea - this was only their third time of meeting, but they already engage in comfortable banter.
I first met Shirley three years ago when UK Donorlink was beginning - and at that time she told me of her longing to meet a half-sibling.
Now she is been able to embark on a complicated but fascinating experience.
"It's like finding a little piece of yourself," Shirley said. "It's like making this little web of connections that hasn't been there before."
The Donorlink project has more than a hundred people on its register at the moment.
Its manager, Lindsay Marshall, says they have been dealing with a wide variety of requests.
"We've been taking calls from parents of donor-conceived adults, who've been saying 'my child was conceived in this way but I haven't told them and they're now 25 and I don't know how to tell them'.
"We've been able to give people quite a lot of support even in that area."
The progression of medical technology is bound to generate ever more complicated ethical issues.
But for Louise, being able to look at a photo of her biological father and to understand her genetic heritage has meant the world.
"I felt shame just come off me - and I never knew that I felt ashamed," she said. "It was literally like something physical leaving me. I just felt I was holding my head up higher."
* Some of the names have been changed, to protect people's identities.