Considering that the US legal system is more or less similar in practice to the English Courts, yes it is possible to plea bargian a deal. I'm linking to the wikipedia article on the matter with a specific link to the England and Wales for guidence. Normally, I'd explain, but I'm an American and the differences between Magistrate and Crown courts are big enough differences that I can't tell you what the differences in the case is.
I should point out this is a legal area where America differences with much of the world. 90% of the United States criminal cases (and a good number of civil cases, which are settled privately before discovery phase) are plea bargained to lesser sentences. Additionally remorse has nothing to do with the plea bargain. You might only be sorry that you got caught breaking the law and can still plea. The lighter sentence is sort of a "thank you" for saving the state money in not having to build their case against you.
It is also used to coerce cooperation with the police, as they may have the accused dead to rights and can prosecute him successfully, but he's a little fish who can give intel to a big fish (this usually comes with the caveat of it being a sworn statement, so they can still prosecute you for something if you're lying... OR that the deal holds on condition that everything is factually true. If evidence contradicts you, you're charged as if you never made a deal). It's also important to note that the police will not honor their deals made for your confession... but they will offer you deals (In the United States, police are allowed to lie to you and do it all the time). However, the prosecutor will honor their deals.
Another thing to be aware of is that a prosecutor who offers a plea could be doing so because they have a weak case. If you are absolutely sure the prosecutor has the wrong guy, it may be to your benefit to go to trial and have them prove it. Innocent people do go to jail all the time because they think there is something worse on them than the plea deal and its hard to fight off as you cannot appeal a plea deal as easily as a court conviction.
Finally, most jurisdictions allow the judge final say at sentencing, so if the prosecutor does honor the deal and advises the sentence, don't get upset if the judge is tougher and gives you a harsher sentence on the crime, or rejects your plea outright (expect him to scold the prosecutor for wasting his time with a horrible deal, too. Watch the Law and Order SVU episode Raw for a particularly wonderful instance of this rare event occurring). As a part of US federalism, the rules about this change from jurisdiction to jurisdiction, so make sure you understand this. Another thing to be aware of is that a prosecutor who offers a plea could be doing so because they have a weak case. If you are absolutely sure the prosecutor has the wrong guy, it may be to your benefit to go to trial and have them prove it. Innocent people do go to jail all the time because they think there is something worse on them than the plea deal and its hard to fight off as you cannot appeal a plea deal as easily as a court conviction.
I would definitely do some leg work into the English Legal system's opinions on plea bargains. Just because they have it does not mean the state lawyers like employing it and many jurisdictions see it as full on corruption in other parts of the world, even the Common Law jurisdictions.