Im sure that as a parent you are allowed so many days a year for your "dependants" but it is at the companys discretion if you are off paid or unpaid.
Have a look on the internet to see what your rights are, www.direct.gov.uk, there is a bit about having time off for dependants: I have copied these bits for you as they might help,
If you are an 'employee', you have the right to unpaid time off work to deal with emergencies involving a 'dependant' - a husband, wife, child or parent, or anyone living in your household as a member of the family. A dependant may also be anyone who reasonably relies on you for assistance. The right is not for long term care arrangements such as childcare or nursing a sick relative.
Your employer doesn't have to pay you for time off for dependants but they may choose to do so. You can check your contract of employment to see if there's a policy about this.