Common law is merely a term meaning that the whole of the law applies. That is to say that in considering any case the whole of the law including legislation and case law must be considered where it applies. This differs from a system of administrative certainty.
As such in saying "English common law" you are really saying "English law" as the English legal system is one of common law.
As such in saying "English common law" you are really saying "English law" as the English legal system is one of common law.