If you have acquired the right to park on private land through long use when you can claim the right either under the doctrine of Lost Modern Grant, or the Prescription Act. Lost Modern Grant is a legal fiction whereby, you have enjoyed a right for so long that it must have been granted formally but the deed has been lost. Under the Prescription Act you acquire the right if you use it without consent and without objection for 20 years or more and you can prove that which clearly is not a problem.
Once you have a right of way or a right to park or any other right, it can only be extinguished by deed if the local authority are taking it over, by having it compulsory purchased.
If however this area that you were parking on, even though it had markings, was highway, then you cannot acquire a right by prescription. Local authority are free to redevelop it in any way that they wish.
You ask whether the right could be extinguished when the council took the road over without recourse to you: it would only have to consult with you if you were claiming the right over it under one of the ways I mentioned earlier. If they had no notice of the right, they would just go ahead and do it and of course what you would do as soon as they started is apply for an injunction to stop them pending the determination of whether you have the right to park or not.
So depending on the circumstances and ownership of this land, you may be able to continue to park on it or the local authority may be able to do with it as they wish.
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