The team examined reports of children's mental health at 3, 5, 7, 11 and 14, including emotional problems such as feelings of low mood and anxiety, and behavioural issues such as disobedience.
They compared information on children who experienced a family split with those who did not. A fifth of children in the study saw their parents separate between the ages of 3 and 14.
Among older children, increased emotional problems were noticed for both boys and girls, but more severe behavioural issues were seen only in boys.
The study also suggested that, after a family break-up, children from more privileged backgrounds were just as likely to have mental health problems.
Professor Emla Fitzsimons, who co-authored the study, said: "With adolescent mental ill health a major concern nationally, there's a pressing need to understand the causes."
She added that older children are also more likely to be affected because disruption to schooling and friendships is often greater.
Published in Social Science & Medicine, the study also investigated the impact of a break-up on mothers' mental health and financial resources.
Across the UK, women accounted for 90 per cent of lone parents, and most children in the study lived with their mothers after a split.
Mothers reported, on average, more mental health problems than those still with their partners if they separated when their children were older.
This is believed to be because the financial impact of divorce was greater the later on in the marriage.
According to the Office For National Statistics, there were 101,669 divorces of heterosexual couples in 2017.
Just over four in 10 marriages in the UK end in divorce.
WHERE TO GET HELP:
If you are worried about your or someone else's mental health, the best place to get help is your GP or local mental health provider. However, if you or someone else is in danger or endangering others, call 111.
If you need to talk to someone, the following free helplines operate 24/7:
DEPRESSION HELPLINE: 0800 111 757
LIFELINE: 0800 543 354
NEED TO TALK? Call or text 1737
SAMARITANS: 0800 726 666
YOUTHLINE: 0800 376 633 or text 234
There are lots of places to get support. For others, click here.