Almost two out of five do not get home in time to say goodnight to their children, a similar number cannot help with homework and one in four blame work for arguments with their partner.
Working overtime was also linked to poor eating habits and not having enough time for regular exercise.
A survey of over 2,700 working parents found that two out of five contracted to work 35 or 36 hours a week were putting in extra hours, falling to a third of those on a 25-hour week.
The report said the findings painted a “worrying” picture for parents, many of whom admitted they were deliberately “stalling” their careers or refusing a new job or promotion for work-life balance reasons.
Sarah Jackson, chief executive of Working Families, said: “For mothers and fathers, becoming a parent looks like a bad career move.
“Because the norm for people who want to get ahead is still to show up early, leave late and be on email out of hours – and parents have less time to give, putting them at a disadvantage.
“Parents are responding to the pressures on them by acting, deliberately stalling and downshifting their careers. With more than 11 million working parents in the UK, our economy can ill afford this ‘parenthood penalty’.
“We need a more widespread, genuinely flexible approach to work. We need human-sized jobs that allow parents to fulfil their labour market potential and give families back the time together they need to thrive. ”
James Tugendhat of Bright Horizons, said: “The UK’s long hours culture is putting severe strain on family life in the UK.
“Many parents are working unsustainable hours to make ends meet, returning home stressed and exhausted. “