There are two schemes that are available, though there are restrictions in both:
The Criminal Injuries Compensation Scheme (CICA) is a government-funded scheme designed to compensate victims of violent crime in Great Britain. To be eligible it requires all incidents to be reported to the police. There does NOT have to have been a court case or a conviction.
Civil Case for Compensation – you can, through the use of a legal representative, pursue a case through the civil courts for compensation. Association of Child Abuse Lawyers can help you with more information about this process and whether it is something you wish to pursue or not.