The road scheme includes a small section of tunnel - even though an earlier programme advanced by English Heritage which ran largely underground was ruled out on grounds of cost.
Relations between English Heritage, ministerial advisers, and the Government, reached a new low last week after the Highways Agency disclosed another proposed "northern" route away from the site in Wiltshire as well as reviving two other rejected schemes.
Jocelyn Stevens, English Heritage's chairman, was said to be "incandescent with rage" when he heard that the two routes - one along the existing line of the A303 and another further south - were back on the table, with yet another "unacceptable" one north of the site.
The search for a solution to the Stonehenge site, which attracted 700,000 visitors last year, comes against the background of predicted increases in traffic, from up to 20,000 vehicles daily in 1994 to as many as 42,000 in 2017.
Mr Stevens, who chairs the joint English Heritage and National Trust steering group on Stonehenge, was scathing about last week's announcement.
"The Highways Agency has produced a northern route that is totally unworthy of a World Heritage site," he said. "We will oppose it until the necessary changes are made to eliminate the destruction of local homes and the environment as well as the archaeology and landscape."
His anger was heightened because Steven Norris, the transport minister, had agreed the two other revived routes were "non-starters" and that he would try to find a solution working closely with English Heritage.
Last week the agency said the southerly by-pass would cost pounds 22m, English Heritage's rejected 4,000m tunnel scheme along the line of the A303 pounds 43m, and its northerly route, pounds 30m.
Despite Mr Stevens's criticism of the agency's new route, the one that English Heritage will outline on Thursday follows much the same line as the northerly plan. But to lessen its impact, it would run slightly further south of Larkhill and would involve an 850m tunnel at Strangways.
"Our main aim with the new scheme is to reduce the impact on local homes," a spokeswoman said yesterday. Equally though, Mr Stevens envisages turning the area with its wealth of monuments into a prehistoric park enjoying some solitude.
However, many fear that a solution to the impasse may yet be far off, particularly after the agency's unilateral decision over the latest scheme.
Richard Morris, director of the Council for British Archaeology, said: "It is amazingly crass that English Heritage has not been consulted. That is their role, to advise the Government."
Some sources fear that the agency's announcement, together with an invitation for further suggestions, may have been a stalling tactic because of lack of cash in government coffers.