Native English bluebells are protected, what a lot of us have got in our gardens though, is the Spanish variety, which are sold in garden centres. They are more thuggish, and not as attractive as our native, and they interbreed with the native ones, or seed in woodlands and crowd out the natives. So we are encouraged to get rid of them from our gardens, particularly where we are close to woodland with the native variety in them.
You can tell a Spanish bluebell because they aren’t such an attractive deep purply blue, don’t have the same scent, and have flowerlets appearing on all sides of the stem, not just one side, so they don’t hang over gracefully like the English ones.