Research has found that fathers in full-time employment earn 21% more than men without children. This is an interesting statistic but relates only to those working full-time. Statistically it seems that men in part-time positions earn on average less than women in part-time roles, although this may be because women in higher paid, professional positions are more likely to seek part-time roles than men in such roles.
It will be interesting to assess the figures when businesses (with over 250 employees) publish their first reports under the new gender pay reporting requirements. Starting in April 2017, they must analyse their gender pay gap and publish their report within 12 months with annual reports thereafter.
It looks like having children helps your career... if you're a man. According to the TUC, men are likely to earn more after they have children, whereas women are likely to earn less.