You don’t need to display blue badges on private land the Equality Act applies here. If you have a disability under the Equality Act and need to use the disabled space you can. Blue badges are hard to get. You can’t get a blue badge for needing a larger space to open doors.
Blue badges are very hard to get in my borough if you are over pension age and not getting PIP or AA. The assessor doesn’t follow the rules. A person with osteoarthritis was told to get a knee replacement instead of a blue badge by the assessor.