Brian and Kerry Ann Howes, from Bo’ness, near Falkirk, are said to have sold legal chemicals which were then used to make illegal drugs in the US.
The pair maintain they ran a legitimate business.
The Court of Criminal Appeal in Edinburgh granted them leave to take their human rights challenge to London.
Defence counsel Chris Shead, for Mrs Howes, told Lord Mackay, sitting with Lord Bonomy and Lord Osborne, that an English case involving parents facing extradition had already been referred to the Supreme Court.
He said that the Howes’ case was an “anxious” one and added: “Her health is under significant pressure while in custody.”
Lord Mackay said the judges would allow leave to appeal on issues relating to Article 8 of the European Convention on Human Rights, governing the right to family life, which had arisen during the Scottish proceedings.
The couple were arrested by Central Scotland Police in 2007, amid claims they supplied more than 40 chemicals to dealers via the online company Lab Chemicals International.
They lost a bid to prevent them being sent to Arizona to face trial at the Court of Criminal Appeal in Edinburgh last month.
The charges against Mr and Mrs Howes allege they used their internet company to supply red phosphorous and iodine to 400 customers in the US, most of whom were producing methamphetamine, also known as crystal meth.
Red phosphorous and iodine are legal in Britain, but regulated in the US.
The case falls under the 2003 Extradition Act which allows the extradition of people to the US without any trial taking place in the UK, removing the need for US authorities to provide prima facie evidence of criminality.
An extradition order was made by the Scottish government on 29 May 2008.
Mr and Mrs Howes face being separated from their children if they are extradited to the US.
This article was published by BBC News on August 11, 2011.
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