The mother of one of the NatWest Three bankers today said her son had pleaded guilty to fraud with "deep reluctance".

David Bermingham, 45, from Goring, Gary Mulgrew, 45, and Giles Darby, 45, told the US district court in Houston, Texas, they wanted to change their plea to guilty yesterday following a deal with prosecutors.

Under the agreement, which has yet to be accepted by the judge, the trio would all serve 37 months behind bars and pay $7.3m (£3.5m) to the Royal Bank of Scotland, which owns NatWest.

In return for the guilty pleas to one charge of wire fraud, US prosecutors would ask for six other charges to be dismissed and support the trio's bid to "serve some of the sentence" in the UK.

The three men were extradited to the US under a controversial treaty 17 months ago.

Today Trish Godman, the mother of Glasgow-born Mulgrew, said: "My son Gary Mulgrew and his two colleagues are the victims of an unjust extradition treaty, which breaches human rights, and a Texan judicial system which has bled them financially dry and coerced them into a plea bargain."

The three men have admitted advising their former employer NatWest to sell part of a company owned by collapsed US giant Enron for less than it was worth.

They then left the bank and bought a stake in the company, Swap Sub, which they then sold on for a huge profit, making about $7.3m each (£3.5m) themselves.

Father-of-three Bermingham, Mulgrew and Darby, have all been described as "ordinary family men" and are known to be keen to return home to the UK as soon as possible.

Outside court, with all three defendants at his side, lawyer Reid Figel said the guilty pleas were "an important first step to bringing this terrible ordeal to an end".

The three men are due to be sentenced on February 22, but Dan Cogdell, defending Bermingham, urged the judge to consider bringing the sentencing date forward.

The three men remain on bail of $4m (£1.9m) and must not leave a specified area of Texas.