Original article says it is £1.7bn for just under 2 miles of tunnel. For comparison, the new Crossrail is £15.4bn for 73 miles including 13 miles of twin tunnels under central London[0].
That's rather disingenuous, the tunnelling contracts for Crossrail's 42km of tunnels came to £1.5b in 2011, or £1.8b today - £40m per km.
The tunnelling was 10% of the total cost of the project.
Stonehenge requires 6km of tunnels, which would be £250m at crossrail rates, if that was also 10% of the total cost that would be a £2.5b project
The tunnels aren't comparable either -- each bore of crossrail is 7.1m, I believe the ones needed for the road tunnels would be larger than that, but on the other hand crossrail project included electrification of the GWR to Reading and resignalling.
Crossrail is also Europe's largest construction project - some of the numbers are incredible, e.g. "Over 3 million tonnes of excavated material from the tunnels was shipped to Wallasea Island in Essex to create a new 1,500 acre RSPB nature reserve"[0]. It also required spending £1bn[1] buying up and demolishing large areas of prime real estate in one of the most densely populated and expensive places in Europe to create 10 brand new stations. Not to mention that "100 archaeologists have found tens of thousands of items from 40 sites, spanning 55 million years"[2]. So the fact that it is more than 10% of the cost of this for a short tunnel under open fields in a sparsely populated area for relatively few people and providing no major new public transport hubs is I think all the more surprising.
[0] https://en.wikipedia.org/wiki/Crossrail