Adding lanes has literally never fixed traffic anywhere ever.
It might fix everyone slowing down to a crawl as they go past Stonehenge though. The a303 is a dual carriageway that goes down to 1 Lane past stone henge, the new tunnel would stop the bottleneck that happens as it goes past stonehenge, if having a busy road that goes past Stonehenge hasn’t affected it’s world heritage status, then changing that to a tunnel shouldn’t affect it either, if anything it will improve the aesthetics as all you can hear there is the road.
The main question should be, could this money be better spent? The answer is obviously yes.
That being said, if the issue is traffic slowing down, then you put up a monument between the highway and Stonehenge that blocks drivers’ view. Could easily be a monument to the Celtic and Gallic history of England. Something nondescript from the road’s side.
If the issue is the amount of traffic, then regulated entry is the way. Put stoplights at the highway’s entry and only let several on at a time.
How to kill your country’s infrastructure 101