Minimum sentences are almost unknown in English law,sir.prize, and with good reason. Drink-drive, for example, has a minimum ban, and certain firearms offences have a minimum sentence given the qualifying circumstances. Murder has one, life, but that is not life as generally understood and never has been.
Manslaughter has a life maximum and is a good example of why we have no statutory minimum. The cases vary so much in their gravity as manslaughter. We rely upon judges using their powers properly. In fact, for all offences in a given category of gravity there is a starting point, departed from only in exceptional cases.