Hello Per-Harald
Despite looking at the planning application I am not sure if the work has been approved or been done. I am sure you can park there but maybe overnight at a stopover as Tom suggests.
As well as Stonehenge there is nearby Avebury, which for me gives a far better experience, less crowded and organised. The problem with Stonehenge is that you can only walk around the perimeter, usually in procession with coach loads of others.
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