The Allens say they bought the twin girls

But the Allens have already indicated they believe the adoption procedures in Arkansas were illegal.

Authorities in the UK and the US are now investigating this, raising the prospect of the twins being taken into care and returned to America.

Legality of Arkansas adoption

The legality of the Arkansas adoption is likely to play a central role in this child ownership battle, according to Naomi Angell, a solicitor with London firm Goodman Ray, who specialise in family law.

She said: "Arkansas is pivotal because if that fails there is nothing to recognise in this country and then the Kilshaws would have to start adoption proceedings at the High Court."

The other battle frontiers are immigration and the question of whether the twins were abducted, as claimed by the Allens.

On the issue of immigration, a couple must apply to the British embassy nearest to where the child lives for permanent admission to the UK.

This should ideally be agreed before the child arrives in Britain.

An application for British citizenship can be submitted afterwards.

But the Home Office said admission to the UK would not be automatic if the child had an interim adoption order, such as the one granted to the Kilshaws in Arkansas last month.

It is understood the twin girls were brought into Britain on the Kilshaws' American passports as temporary visitors.

Each case is decided on its merits and there are grey areas in the law which can allow parents who have not followed the correct procedures to keep the adopted child.

On the issue of whether a possible abduction charge is brought, there is an international convention on child abduction which would be used to decide if the Kilshaws had violated the law.

Another possibility is the children could be made wards of court in the UK and either side in the dispute could decide to institute proceedings, which would result in the girls being taken into care.

The most important question though in all of this is what is best for the children?

"What one really hopes, regardless of the rights or wrongs of the adults, you have to look at the fact that these children wil have moved four times and they're only six months old," said Naomi Angell.

"If they become wards of court the babies' best interests would be paramount; the wishes of the adults would be secondary," she added.

The Allens could decide to go to court in the US or Britain, and are said to be considering both options.

Amid all the legal wrangling, one fact remains: the longer the children stay with the Kilshaws, the stronger their case and as the weeks pass, a judge could decide that removing them would harm the children psychologically.