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The Lower Thames Crossing "will not be the answer to all our prayers", warn councillors.
Controversial plans to build a 14-mile link road from Kent to Essex by 2030 remain on the table from National Highways, which will cost between £6.8bn to £8.2bn.
Today the transport authority released an animation which it says shows the "unprecedented" levels of traffic that use the Dartford Crossing every Friday, causing frustration for tens of thousands of motorists.
Dartford East county councillor Penny Cole (Con) has urged National Highways to provide extra funding to ease that congestion.
She said: "I think the Lower Thames Crossing will help, but we have to wait 10 years for it to be built.
“The money that is coming to Dartford is not enough. I would like to see more."
Opening in 1963, the Dartford Crossing is one of the busiest transport road links in the UK as it connects key ports and manufacturing centres.
National Highways says more than 50 million vehicles use it every year, with more than 180,000 vehicles making the journey on its busiest days.
Almost every weekday, 95% of northbound journeys are delayed during the evening peak with almost two thirds of journeys taking at least twice as long as they should.
Tailbacks regularly reach 10 miles into Kent.
It also has one of the highest accident rates of anywhere in the UK, with 3,000 prangs every year.
The proposed Lower Thames Crossing aims to ease traffic issues there by taking 13 million vehicles off the Dartford Crossing each year.
Matt Palmer, who is the executive director of Lower Thames Crossing, says there is an "urgent need" to address the traffic problems in Dartford.
He said: "The best and only solution is the Lower Thames Crossing.
"It will take more than 13 million vehicles off the Dartford Crossing each year, meaning journeys across the River Thames will become quicker, more reliable and less stressful.
"The benefits will be felt by businesses and individuals alike as new opportunities open up, as a result of reliable journeys."
National Highways is preparing to send an application to the government to review the tunnel project, which would be built east of Gravesend.
If approved, the Lower Thames Crossing is anticipated to be constructed in 2024 and open to traffic in 2030.
Dartford North East county councillor Kelly Grehan (Lab) says the design of local roads needs to be improved on the approach to the Dartford Crossing,
She has urged road designers from the Department for Transport (DfT) to visit Dartford.
Cllr Grehan said: "The Lower Thames Crossing stops things getting worse, but traffic is at a stage where it is not enough to deal with the congestion alone."
She added: "We should expect some compensation for people living in Dartford. The government have really abandoned to deal with this crisis alone."
Calls have been made for more funding to be made available from National Highways for footpath improvements, tree planting and vegetation.
Cllr Cole added: “The Lower Thames Crossing is not going to be the answer to all our prayers because the volume of traffic that is going through the tunnel is large.
“When travelling at peak times and there is an accident, it is still going to create traffic problems in Dartford."