This is one of a number of old British law terms that have formally been made redundant through the reforms to the system of civil justice that came into force on 26 April 1999.
A part of the attempt to make British civil law more relevant has been to sweep away its obscure language, such as plaintiff, writ and affidavit. But surrebutter was already defunct for practical purposes in British legal use, so its loss will not be regretted, or even I suspect much noticed.
In the old process of common law pleadings, there was a set sequence of claims and responses by the lawyers on each side. The person who brought the action (the plaintiff) made a declaration of his case; the defendant then made a plea in response. Depending on the complexity of the case, there could be a further round, in which the plaintiff uttered a replication and the defendant a rejoinder. The next pair was called a surrejoinder and a rebutter. If a further step were needed (you’re still with me, I trust?) we then had a plaintiff’s surrebutter.
A writer in the old British newspaper, the Daily News, remarked in 1888 that “Controversy is seldom profitable after it gets down to the stage of surrebutter and surrejoinder”.
The prefix sur– here is a form of super–, which you will find in surcharge and surpass as well.