Ask an Property Solicitor. Get an Answer ASAP.
Hello, I am a solicitor with 20 years experience. I will try to help you with this.
I am assuming the injunction threat has come in writing. Have you replied to the HA pointing out their error and if so what has been their response.
If you have a legal right to park there I fail to say what they can do about it.
How is your legal parking right enshrined is it as part of your tenancy agreement with your parking slot described or is it in some other document? In order to justify the cost and effort of getting an injunction they would need to show that there was harm being caused. Have they said you are causing any and if so what?
I think the original architects drawings are likely not to be binding unless included in the tenancy agreement. What the architect intended is not always reflected in the actual living arrangements. However the architect's view is likely to be relevant to whether It sounds like there is a general right to park where ever you want as long as you are in a parking space.
Unless there is some special issue, eg. you are parking a van or minibus towering over their home or the neighbour is disabled and needs the closest spot I can't see any action the HA can take against you.