More British men are asking their employers if they can work flexibly, but are more likely than working mothers to have their requests turned down by employers, unions have complained.
Research by the TUC has found that, while men are still less likely to consider changing their hours than working mums, they are becoming more prepared to at least ask the question.
But the answer from employers is more often than not "no", it said.
The TUC is calling for a whole new approach to the way work is organised in the UK, including making greater flexibility over working hours an option for all employees, not just parents and carers.
In the first two years that the right to request to work flexibly has been in existence in the UK for the parents of children under six, around 10 per cent of male employees have approached their bosses about changing their working hours.
In the same period, 19 per cent of women in work requested flexible working.
But bosses looked more favourably on requests submitted by their female members of staff, it also found.
Only 10 per cent of women had their requests rejected out of hand, compared with 14 per cent of men.
Just a handful of those who are rejected ever take their employer to an employment tribunal, and claims submitted by men are much less likely to be successful, the TUC added.
Male claimants accounted for just over a quarter of flexible working tribunal claims but nearly half of the cases were lost, ruled out on procedural grounds or dismissed.
The reluctance of employers to let more of their male employees change their hours in some way after they become parents is reinforcing the idea that it is the working mother who has to reduce her hours and juggle childcare and work when her children are young, said the TUC.
As a result, women end up paying a part-time pay penalty, will often be in a job well below their skill potential, and lose out when it comes to future pensions' payouts because of the time they have spent out of the labour market, it argued.
Fathers are also forced to work longer hours to compensate for the loss of family income as their partners switch to part time working.
TUC general secretary Brendan Barber said: "Many UK bosses are too short-sighted to grasp the fact that a flexible approach to work is not something to fear as expensive and irritating, but a change which makes sound business sense, both in terms of company profits, and staff recruitment and retention.
"The UK's long hours culture will never be challenged if it's only parents and carers who can ask to change their hours, and if it remains all too easy for inflexible employers to say no," he added.
"By accepting flexible work requests from their female employees but not from their male staff, employers are helping reinforce the gender pay gap, when instead they could be enabling young dads to play a more active role in the raising of their children," he concluded.