I presume you mean shoulder fired arms? In 1883, they weren't quite there to issuing repeaters. The Martini Henry in all it's glory was still the standard battle rifle of Great Britain. Five years later, it would be replaced by the Lee Metford rifle, which was replaced by the Lee Enfield in 1895.

As for the accuracy of the Martini, they were certainly military accurate, and were popular target rifles, you'd need to be more precise on what you mean by "accurate" though please.