The key difference is Criminal law is imposed as an automatic obligation (or rules and standards of behaviour) for any British Citizen residing under the crown, therefore crimes such as theft or burglary will be pursued through the criminal courts against a defendent by Her Majesty's 'Crown Prosecution Service'
Civil law, on the other hand, is the law of implied or written obligations (such as Contract and Tort Law) between private citizens not acting in the interests of the Crown.