Negligence plays a minor role in criminal liability. It used to form the basis of some driving offences but this has largely been superseded by recklessness. Negligence adheres to an objective standard. This is strictly applied:
McCrone v. Riding [1938] 1 All ER 137 Case summary
The main role for negligence in criminal law is with regards to gross negligence manslaughter. This requires the prosecution to establishe that the defendant owed a duty of care, was in breach of duty which resulted in death. The current test for establishing liability for this offence was set out in: