Despite months of fierce campaigning, the scheme - which will see the road turned into a dual carriageway - is likely to go ahead.
Members of the cabinet, who met yesterday afternoon, also pledged to replace any trees which have been felled on a two-for-one basis.
More than 20 protesters turned up to the meeting at the Civic Centre in Victoria Avenue, Southend, prompting it to be moved to a larger committee room.
The widening of Priory Crescent, with improvements at the bottleneck Cuckoo Corner roundabout on the A127, is a cornerstone of the Local Transport Plan.
Technical services director David Watts warned the whole £36 million package of Government investment could be at risk if it was not agreed. But in recent months, there have been furious rows over the scheme, which could have cut into Priory Park. It has since been amended so the road itself does not touch the park.
Under the new plan, an area of land between Priory Crescent and the Liverpool Street to Southend Victoria railway line will be affected - and a number of trees felled.
He said: "We are trying to protect the trees, but the campaign has done damage.
"We are not going to bulldoze a road through Priory Park, as many protesters who signed petitions seem to think. If this was the case, then I would be out in the public gallery with them, not here supporting this scheme."
Cabinet member for regeneration, David Garston, said he used the park frequently but was concerned businesses in the east of the town were suffering because of congestion on Priory Crescent.
Ann Holland (Con, Southchurch) asked if the Cuckoo Corner roundabout improvements could be carried out in isolation.
She was told by council officers it was possible - but it could put the whole transport plan in jeopardy.
The cabinet's backing for the scheme will now go before scrutiny committees before a final decision is made by the council in April.
Opposition Labour and Liberal Democrat groups are likely to oppose it.