You can blame the Normans for introducing them in the first place! There's some argument as to whether or not it was the Romans - but there's no real evidence that they used them in the way that the Normans did - i.e. for meat and fur. It certainly was the Normans who created special rabbit enclosures - "warrens" - and although some rabbits did escape, they didn't last long outside the warren as they were caught and eaten by the peasantry, who were only too glad to find a source of meat. As far as I know rabbits were one of the few wild creatures which they were allowed to hunt/trap without getting into too much trouble with the local "landlords".
I'm not sure about when "myxi" was introduced into the UK - it certainly wasn't what you'd call "an issue" when I was a child. I wonder whether it was another deliberate introduction, relatively recently & perhaps from Australia, because the introduction of rabbits there caused a great problem too. Apparently myxi is spread via fleas and passes from one rabbit to another when they are underground in the burrows and come into close contact with one another. I don't ever remember anyone mentioning myxi in hares and this is probably because their habits are somewhat different and they don't go underground at all.
Although there have been several myxi outbreaks round here in the past few years, it doesn't seem to be nearly so severe in its effects as was once the case. Perhaps those rabbits which survived it in the past developed some sort of immunity. I think it more likely that the survivors were in fact those rabbits which were "outcasts" - in that they spent less time underground in a group than most did. Their habits have certainly changed, in that years ago I never saw rabbits other than at dawn and dusk. Now I see them in my garden, in the adjoining lanes, & on my lawn throughout the day and have come to the conclusion that perhaps this is an inherited trait from those earlier survivors. Nowadays they're somewhat smaller too - again maybe an inherited trait from the weaker "outcasts". Perhaps one of the few times when the weakest - rather than the strongest - survived.