The offence of murder is committed when a person takes a life with intent. The intent may have been only to harm, but if the victim dies, the crime is murder. The intent does not have to be premeditated. A spur of the moment killing is still classed as murder, provided the intent is still there. Manslaughter is the taking of a life without intent to do so. So, if a man deliberately fires a gun at a group of people, killing one of them, he has committed murder, since, by aiming, he intended to do harm. If he was carrying the loaded gun, tripped and unintentionally pulled the trigger, killing one of them, the offence is manslaughter. That is why motive to kill, leading to intent to kill is very important in cases of murder.
In 1910, the mandatory sentence for murder was death by hanging. The judge had no discretion. The law insisted that he place a square of black cloth (the "black cap") over his wig and say:
" Name of the accused, you will be taken hence to the prison in which you were last confined and from there to a place of execution where you will be hanged by the neck until you are dead and thereafter your body buried within the precincts of the prison and may the Lord have mercy upon your soul".
If a person pleaded guilty to murder, they were still sentenced to death. A guilty plea merely saved the court's time. If there were mitigating circumstances (e.g. the killer acted in self-defence, or in defence of another person) and this can be proved in court the mandatory death sentence could be commuted to a suitable term of imprisonment (usually life, but the actual circumstances could mean a lesser sentence.) The power to commute a sentence, once passed, lies only with the Secretary of State for Home Affairs (aka the Home Secretary.) In a colony, sometimes the Governor of the colony was given the power to commute sentences.
A person found guilty of murder, or pleading guilty to the offence, and sentenced to death had the right to appeal against the conviction and/or the sentence, but the Appeal Court was very likely to uphold the conviction and sentence, on the grounds that, if someone pleaded guilty to murder, they had admitted the crime and, if they had pleaded not guilty, but were still convicted and sentenced, that all the evidence and arguments had already been weighed by a properly-instructed jury and the decision of the court was just.
Plea-bargaining per se doesn't really exist in English jurisprudence. A prosecution will only be brought if the prosecuting authorities believe that there is a strong chance of a conviction. If that is in doubt, the accused will not be charged with the offence. If there are lesser charges which can be more readily proved, the accused would be charged with those.
If the accused has co-operated fully with the investigating and prosecuting authorities and shows true remorse, these days, this will be taken into consideration by the court and may result in a lighter sentence, but this rarely happens in cases of murder. An accused person who committed murder in concert with others can turn "King's / Queen's evidence," where he enters into an agreement with the prosecutors to testify against his accomplices. This would not result in him/her walking free, but would often result in the person turning "King's Evidence" being sentenced to a term of imprisonment, or in the 19th century, transportation, while those against whom he testified were hanged. Full immunity was/is rarely if ever granted. The main exceptions to this are the modern "supergrasses," professional criminals who agreed to testify against numbers of high-level criminals in exchange for immunity from prosecution. The granting of immunity to one, or two individuals was considered a price worth paying to break up gangs of organised criminals and put many of their leaders and members behind bars for a very long time.
The ancient "Year and a day rule" wasn't repealed in England until 1996. Until then, if the victim of an attack died of his injuries more than a year and a day after the attack, his assailant could not be charged with murder.
So,with apologies for the length of this post, in 1910, under English law (I say English, rather than British, as the Scots have a somewhat different legal system - but not with regards to murder.) if your character pleads not guilty and claims self-defence, but his claim is later disproved to the satisfaction of the court, he will undoubtedly hang. If, at first, he claims self-defence, but changes his plea to guilty when told that there is evidence to disprove his claim, he will still hang. The intentional killing of an unarmed man by one who was armed has to be a case of murder, even if the victim had attacked the accused first. The lethal use of a weapon to defend oneself against an unarmed assailant is considered to be in excess of what, these days, is called "the use of reasonable force" to fend off the attack. So, whichever way you look at it, your character would be facing the gallows. Sorry.