Is there an order parental leave needs to be taken in?

There’s no specified order for maternity leave, paternity leave and shared parental leave. They can be taken simultaneously if needed.

However, leave needs to be taken:

Within 12 months of the child’s birth, for shared parental leave.
Within 12 months of the child’s birth, for maternity leave.
Within 16 weeks of the child’s birth, for paternity leave, unless otherwise agreed with the employer.