In a ruling likely to have far-reaching implications for hundreds of people with outstanding civil debts, Mr Justice Keene overturned the sentence imposed on the man by Stafford Justices on April 4 1998.
The judge also substantially reduced the sum the man, who is in poor health, now owes in maintenance arrears, ruling that the 16 years it would take to clear the debt - or else be sent to prison - was too long.
But he upheld an earlier ruling by the magistrates that the man, who cannot be named for legal reasons, was guilty of 'culpably neglecting' to pay£9 a week in maintenance for his daughter, who is now aged 15.
On November 20 the same year the weekly maintenance payments were reduced to pnds five, but the magistrates ordered him to pay an additional£4-a-week to reduce the amount of his arrears.
But the man, who suffers from a heart problem, kidney disease, depression and diabetes, contined to pay nothing at all, the court was told.
On 15 April 1998, the magistrates ruled he had made no maintenance payments since July 9, 1996; he had been 'untruthful' about his financial situation and his expenditure exceeded the amount he said he received in benefits.
'The appellant's priority should be his child but he was attempting to avoid that responsibility,' said the justices in their ruling.
'By paying nothing at all, when he was clearly in a position to have made some payments,' the justices concluded he was guilty of 'culpably neglecting' to pay his child's maintenance.
His record of not co-operating with earlier maintenance orders showed 'he would not pay unless coerced into doing so', the magistrates said.
A suspended 28-day prison sentence was imposed on the man, and the magistrates reduced the amount he should pay in arrears to a£1-a-week - in addition to his£5 weekly maintenance payment.
Mr Justice Keene accepted arguments from the man's barrister, Ian Wise, that the justices should have explored other options - such as making direct deductions from the man's bank account - instead of prison.
'The power to make an order, in respect of a suspended sentence for a civil debt, is to be excercised with great caution and only if there are no other alternatives.
'The onus therefore is on the magistrates court to investigate the possibility of such alternatives before it resorts to imprisonment.'
He also accepted submissions that the 16-year period it would have taken the man to discharge his accumulated debt in maintenance arrears was 'unreasonable'.
'An order that could endure for 16 years through all of which time imprisonment would remain as a sanction hanging over this individual's head must be unlawful and must therefore be quashed.'
Mr Justice Keene highlighted the fact that in criminal cases, an individual could only be ordered to pay a fine or order over a two-year period.
He accordingly reduced the sum the man now owes in arrears from£693.50 to£104.
The reduction would allow him to repay the debt, at a weekly rate of one pound, over two years.
Outside court, the man's legal representative, Tracey Jenkins, welcomed the decision.
'This ruling means that people like my client who could not pay the arrears off in a reasonable time - that is about two years - in line with criminal cases, should have their arrears remitted so that a realistic order can be made.
'To have a prison sentence hanging over an estranged father's head for many years is simply wrong, especially when it is considered that such an order could not be made when somebody has committed a criminal offence.
'This principle also applies to the enforcement of other civil debts, such as poll tax and council tax. This will have far-reaching consequences for the enforcement of other forms of civil debt.'