In fact, not only could you challenge me to a fight, you could even get your 250-pound neighborhood brute to fight on your behalf. Now, Bruiser had to go into court and swear that his father on his deathbed had said "Bruiser, son, if you ever hear about a lawsuit over that patch of land down by the pond, I want you to go put it right, do you hear me?" but there were people hanging around the courts who'd swear to anything for enough money.
Little wonder, then, that I'd go to great lengths to avoid those particular lawsuits which could result in trial by battle. Over the centuries, those forms of legal action which didn't have trial-by-combat escape clauses gradually displaced those that did. By the 14th century or so, actual battles were rare events. By the middle of the 17th century, trial by battle was a formality, an option mentioned in the language of court documents, but never used in practice.
Until 1818, that is. Abraham Thornton was prosecuted for the rape and murder of Mary Ashford on her way home from a country dance. The jury acquitted him, to public outrage. English law at the time, since it had descended in an unbroken line from Norman law, without any intervening systematic reforms, was full of oddities and seeming redundancies -- like trial by battle, for example -- so Mary Ashford's brother William was able to "appeal" Thornton, essentially bringing a private criminal suit against him.
To this appeal, Thornton replied by asserting another one of those oddities, trial by battle. William Ashford was a scrawny fellow, in no shape for a potentially mortal combat and he objected strenuously to the use of a fatal feudal procedure which had lain dormant for two hundred years. The judges thought about the question -- for five months -- before ruling that trial by battle had never been officially abolished. Thornton walked.
Trial by battle was officially abolished in short order.
(Information taken from Glanvill (a 12th century English lawbook), J. H. Baker's An Introduction to English Legal History, and The Complete Newgate Calendar)