Rabbits are not native in the UK. They were introduced about 1000 years ago. the first Myxomatosis outbreak in the uk was in 1953. There have been various foolish uses of this disease (the Iberian Lynx is largely only threatened with extinction because it relied heavily on rabbits for food, and these disappeared when myxomatosis was introduced.
Hares are a native species, so it is of greater concern if they are being eradicated. More than 1100 hares have been identified as having died from this, over the last 4 years. Now, as they currently have a population of more than 800,000 individuals, this is not currently a big concern. However if the outbreak has a similar impact to rabbits, then hares could disappear from parts of the UK.
It is already thought to have lost 80% of its population over the last 100 years.
Unfortunately, with our modern habit of farming breeds of wild species, we are giving perfect conditions for new viruses to appear.