Twickenham could miss out on the Gloriana, with Brentford waiting in the wings, if there is widespread opposition to the council's proposals.
Richmond Council's plans to provide a permanent home for the Queen's diamond jubilee barge at Orleans Gardens have been met with hostility from campaigners.
A consultation with residents was launched this month and runs until the end of August, but no planning application has been submitted.
Leader of the council Lord True, who previously criticised opponents for spreading "wild rumours", remains bullish that the Gloriana will still come to Twickenham.
He said: "I have got no sense that the Gloriana people or Lord Sterling would wish to go anywhere other than Richmond, I think they see it as a natural home.
"If the people of the borough said this site didn't work, they might well look at other locations and not just in this borough.
"I hope it does not come to that but I am unrepentant about the opportunity to give this to the borough."
He added said he was frustrated by the stream of rumours being spread about the proposals.
One such rumour this week was that Marble Hill Park could be built on to provide a car park for the site.
The council immediately scotched the suggestion as "totally false" while English Heritage, which owns the land, confirmed there were no plans for development.
With Lord True admitting Gloriana and Lord Sterling could yet be forced to consider their options, the Brentford Chamber of Commerce has called for the boat to come to their town.
Brentford Chamber of Commerce president Suzie Betlem said: "We are interested as a chamber, - Gloriana was built here so it would pretty much be coming home.
"It would be good for our local businesses and could possibly be put in an already developed part of Brentford.
"Gloriana was built in Brentford, was launched very close to Brentford and we would welcome her back."
The chamber plans to talk to Hounslow Council and the Canal and River Trust.
A Hounslow Council spokesman said: "We are more than happy to support the campaign to bring the Gloriana back to its rightful berth in Brentford.
"We will work with the Brentford Chamber of Commerce and all relevant authorities to help make this happen.
"The Gloriana’s presence would be a great addition to Brentford’s successful regeneration and would act as a real pull in tourism terms."
This week, schoolchildren visited the site in question at Orleans Gardens for a "picture party" and sketched the idyllic river vista.
Friends of Orleans Riverside spokesman Paul Bigley said the council would destroy an area of natural beauty.
He said: "We are concerned that this is a pre-determined decision and this so-called consultation is only going through the motions before it goes to planning.
"The council will destroy an area of natural beauty and legally protected views, axe many trees, upset the local ecology, create a deep canal next to a playground, increase existing traffic issues as this area is accessed down a narrow one way street originally intended for horses and carts - the list goes on.
"We may be the last generation to have the privilege of this historic view and experience this tranquil oasis of a park - no one can understand the logic for choosing this site."
A Richmond and Twickenham Times online poll, to which 321 readers responded, found that only 21 per cent of voters supported the current plans.
A similar poll on a Brentford news website, getwestlondon.co.uk, found that, as of Wednesday, 95 per cent of people supported the Gloriana residing in Brentford Lock.
A Port of London Authority spokesman said: "We are aware of the outline proposals but have not received a formal application.
"It is therefore too early to form a view but if and when the idea moves forward, we would at that stage consider all relevant issues that any detailed plan might raise for us as the river authority."