Petitions will be delivered by hand to both the Guildhall in Hull and County Hall in Beverley by organisers of a recent successful protest march.
Both Hull and East Riding councils are looking at extending deadlines for receiving objections on the incinerator, planned for a site near Saltend, which will burn 240,000 tonnes of household waste a year, following complaints from parish councils and Beverley and Holderness MP Graham Stuart.
Hull Council said yesterday the cut-off date was now August 14.
A spokesman for Hull and East Riding Opposing the Incinerator, John Dennis, said: "The next step is that we will handing in our petition, which already contain thousands of signatures, at the Guildhall in Hull and at County Hall in Beverley next Thursday so councillors who will be making the decision can be made aware of the strength of public feeling against the proposal.
"We have got momentum and we are feeling good.
"There's lots of lobbying taking place and objections sent in not only by HOTI members but everyone we can persuade to do so. People are coming into the office with bundles of post."
Coun Dennis said they were putting on buses to take people into Hull and Beverley and urged as many objectors as possible to come along.
The local authorities insist that people made their choice when they voted in a survey last year for incineration and higher recycling.
But campaigners say the process was flawed and the outcome unreliable.
Coun Dennis said: "Nothing is written in stone if people don't want it. I'm afraid things that have been written in the past can mean nothing if the local community doesn't want it to happen. Look what happened to the incinerator on the western side of Hull – it was turned down on appeal."
He says there are many grounds of objection – from it being the wrong waste strategy to the incinerator's impact on traffic in the city centre and Marfleet.
Its impact on the 850-year old grade one star listed St Augustine's Church, in Hedon, just a couple of miles away, was another factor and there were concerns about the plant's effect on an underground aquifer supplying drinking water to the surrounding area.
Last month's protest march from Hull Road, Hedon, to the flyover at Saltend attracted around 600 people.
The incinerator – with a chimney at 95m (311ft) even higher than the Saltend cooling towers – will emit 22 pollutants, but Waste Recycling Group, who will run and operate the plant, claims the amounts will be "tiny" and meet all air quality standards. Tests to judge long-term exposure to heavy metals, dioxins and furans, toxic substances produced as a by-product of burning, concluded they did not "pose unacceptable risks".
People are also worried about waste being shipped to the site. WRG insists it is not looking at importing waste, but the application itself says there may be "surplus capacity" for "suitable non-hazardous waste".
The Hull event will be at 11.30am followed by the Beverley visit at 1pm. Anyone who needs a ride should telephone 899692 by next Tuesday as places are limited and on a first-come, first-served basis.
Petition sheets need to be sent to Graham Stuart MP at his office at 9 Cross Street Beverley HU17 9AX or handed to any HOTI member by Tuesday. Objections can be filed on-line at the website www.hoti.org.uk
alex.wood@ypn.co.uk