Labour pledges to double paid paternity leave from two weeks to four weeks, and increase statutory paternity pay from £120pw to £260pw. We can do simple reasoning about the short- and long-term effects: to begin with it's a benefit for workers, and then contracts adjust to take it into account as they are re-negotiated across the economy. Since it costs the firm more than it's worth to workers wages go down by more than the benefit, workers lose out and firms may lose out.
But maybe there are positive externalities—i.e. even though the workers are more or less bound to lose out, maybe there are benefits to other people (like their children, their families, or society) that are not accounted for in their market decisions there.
Thankfully we have evidence from other countries, principally Scandinavia, as to what effects. These reforms might have. A 2011 paper looking at the Norwegian reforms found that they did nothing to affect labour market outcomes (and may have widened the division between men and women) and nothing to affect kids' schooling outcomes.
However a 2010 paper (newer, gated version), also looking at the Norwegian reform, found that extra paternity leave led to extra long-term involvement with children, to the detriment of their labour market outcomes—lifetime earnings dropped 2.1%.
Other evidence suggests that paternity reforms affect the household division of labour, making it more egalitarian, in a way that lasts. Iceland evidence suggests this leads to lower divorces and narrower wage divides twixt men and women.
In general we see roughly the same results for men as for women but the case is not open and shut—if people have a strong preference for women and men to be have more similar careers then the external benefits may outweigh the cost to the affected workers.