Trandar Wecker, the children's natural mother

But she is said to bitterly regret it, and has started legal proceedings in the UK to try to get them back.

It is understood that Ms Wecker, a 28-year-old former hotel receptionist from St Louis, Missouri, blames her troubled relationship with her estranged husband Aaron for her decision to put the girls up for adoption.

She is being investigated for fraud - accused of continuing to claim child welfare payments after handing over the twins.

She has admitted using the address of her aunt in the adoption of the girls by a British couple, to bypass an Arkansas state law that says the birth mother or the adoptive parents must live in the state for at least 30 days before the adoption.

Aaron Wecker:

The girls' natural father has begun two legal actions in the United States for custody of the children, alleging they were abducted.

Last month a judge in the US state of Missouri awarded custody of the twins to Mr Wecker although it has no immediate effect in Britain, where the twin girls are currently in the care of Flintshire social services.

According to the St Louis Post-Dispatch newspaper, a Missouri judge awarded Mr Wecker custody after he alleged the girls' natural mother had neglected them by trying to sell them over the internet.

Richard and Vickie Allen:

The Californian couple say they paid a San Diego-based internet baby broker, Tina Johnson, $6,000 (�4,000) for the twins last October.

They brought up the girls for two months and accuse the girls' natural mother of snatching them back in December on the pretext of saying a final goodbye.

They have mounted a legal challenge in the US, challenging the adoption procedures in Arkansas that then handed the girls to a British couple.

Their lawyer argues that the adoption was illegal because the natural mother did not fulfil the state's residency rule.

Alan and Judith Kilshaw:

Alan and Judith Kilshaw, from Buckley, in north Wales, paid Tina Johnson $12,000 (�8,000) for the girls.

The Kilshaws have been vilified by the British press

The Kilshaws then drove with the girls' mother, to Little Rock, Arkansas, where they hired a lawyer and began adoption proceedings.

The adoption was granted on 22 December.

The couple then took the girls to back to Wales, to their converted farmhouse a few miles outside the town of Buckley in Flintshire. They named the girls Belinda and Kimberley.

Mr Kilshaw, a 46-year-old solicitor, and Mrs Kilshaw, 47, married eight years ago and have two sons - seven-year-old James and Rupert, four. Mrs Kilshaw also has an 18-year-old daughter, Cayley, from a previous relationship.

But they were desperate for a baby daughter to complete their family. They tried IVF treatment but it was unsuccessful. Believing they would be too old to adopt successfully through official channels, the couple decided in February 1999 to advertise for an egg donor.

One woman came forward but for some reason - the exact circumstances are unclear - the arrangement quickly fell apart. It was then that they turned their attention to the internet.