Tory Cabinet members unanimously agreed the proposals on Tuesday despite a storm of protest around the town.
No land is to be taken from Priory Park itself to make the road into a dual carriageway, the council has assured.
But a dispute has broken out about an area of land containing trees on the other side of the road, which would be affected.
Lib Dem leader Graham Longley, who also represents Blenheim Park ward, said: "Priory Park was given to the town - and we believe the town itself should make a decision on its future.
"There are other alternatives to this dual carriageway and many people may say they do not want a new road of any sort at all.
"Our position has always been, and remains, that we want a local referendum so the situation can be resolved by a vote of the people of Southend."
Mr Longley said he would be asking for the cabinet's recommendation to be brought before the council's environmental scrutiny committee, which meets in two weeks time.
A final decision on the scheme is to be made at the next full council meeting in April.
Meanwhile, the Conservative administration pledged any trees which have to be removed because of the widening would be replaced on a two-for-one basis.