Raise a glass of champagne to Alison Sharland and Varsha Gohil, who have won their supreme court case to force their lying ex-husbands to pay out a fair divorce settlement.

As a feminist cause, this may lack a certain tug on the heart-strings in the long list of women’s wrongs. You may not worry whether Mrs Sharland’s £10.3m settlement was enough, but as she said, she has struck a blow against men who cheat. She found her estranged husband had lied about his income and assets, when it emerged his true worth was estimated to be as much as £656m. Mrs Gohil had settled for £270,000 and a Peugeot, only discovering her husband’s true wealth when he was jailed for money laundering, with £35m hidden away from her.

These cases, with their mega pay-outs, usefully catch the headlines on an issue that matters desperately to hundreds of thousands of women who never get their children’s fathers to pay their fair share of child maintenance. This opens the floodgates, as for the first time women are allowed to reopen old settlements that relied on their husbands’ deceit. Lady Hale, passing the supreme court’s judgment, said: “This case is one of fraud. It would be extraordinary if the victim of a fraudulent misrepresentation in a matrimonial case was in a worse position than the victim of an ordinary case.”

Yet it happens all the time, usually to mothers and children in desperate straits. (Most parents with care are mothers.) Cheating fathers avoid paying up in large numbers, disguising their incomes in devious ways. Here’s the shocking fact: only 52% of separated mothers have any arrangement at all for fathers to pay towards their children. When fathers do make an arrangement, sums are low: the average is £35 a week, according to Gingerbread, the single-parent campaigners.

The history of the Child Support Agency has been disastrous since its bungled introduction in 1993. That Tory government thought they could ease the welfare bill by chasing non-paying fathers – and after disregarding all expert advice, the net result was worse than the previous system. Since then, a backlog of £3.8bn in unpaid arrears has built up, most of which will never be paid to mothers. Labour reformed the system and it improved: it may improve again under the new Child Maintenance Service (CMS), whose computers seem finally to work.

But in the transition, all CSA cases are being closed and mothers have to start all over again applying to the CMS, many fearing the disruption means fathers will stop paying, or the long handover will leave them strapped for months. Only a third of backlog cases with children still young are being “prioritised”, so most fathers will probably get away with their vast arrears. The CMS charges mothers £20 – and if fathers don’t pay, they get their earnings attached plus a 20% extra penalty collection fee. Outrageously unfairly, mothers also get 4% docked off the sum to pay collection costs.

Why do nearly half of all fathers make no payments? Sometimes mothers fear fathers’ anger if they demand money, preferring to keep a reasonable relationship for their children’s sake. Some mothers are victims of abuse. Some fathers may be genuinely penniless. Some occasionally help out with gifts or small sums, and mothers settle for that, rather than causing trouble.

But large numbers of fathers cheat the system quite easily. Although the CSA/CMS can ask HMRC what a man’s income is, many find ways of hiding it. Legally, fathers can declare themselves self-employed for tax purposes, be they taxi drivers or company directors. They can put large sums into pensions, only drawing a small income while calling the rest “dividends” to family members running the company, or they use complex rental income and mortgages to reduce their official taxable income to near zero. That’s OK with HMRC, riddled as it is with loopholes and reliefs – but it leaves almost nothing payable to mothers. If a mother complains that his lifestyle, holidays and cars are not reflected in his declared income, the CMS tells her to call the HMRC tax cheats hotline – but Gingerbread says they get a dusty answer: HMRC complains about all these calls, and says it has bigger fish to fry.

Look at the various fathers’ websites, and many advise maintenance dodging. Fathers4Justice says: “We strongly support non-payment of child maintenance if your are [sic] being denied access to your child.” Access is, of course, decided by courts in the child’s interest, quite separate to maintenance. (For some reason their site is also organising demos at showings of the film Suffragette.) Even in CSA-arranged cases, only 70% pay their full due.

Whatever the system, nearly half of absent fathers pay nothing for the upkeep of their children. Repeat that over and over again. Plainly, avoiding payment is socially condoned by those around them - won’t-pay fathers are not shamed. That’s one reason why single mothers are twice as likely to be poor as the rest. Alison Sharland may be millions of pounds away from the world of mothers who use foodbanks, struggling to work while benefits and tax credits are cut, but she and Varsha Gohil have sent a signal to men who think they can lie their way out of paying what they should.