Bradford MP Judith Cummins told the Commons this week that residents in the city are 'plagued' by quad bikes.
She said the Government needs to take action look into the banning of quad bikes on the road.
The Bradford South MP, said there is 'enormous disruption' caused to the residents of Bradford South because of people on the four wheeled vehicles.
She said: "People are plagued quad bikes driving up down our roads and pavements – often with facemasks and no licence plates.
"The government needs to do something to tackle this, specifically with legislation."
But Commons Leader Mr Rees-Mogg, an MP for North East Somerset, refused to commit to it being looked into.
He said: "I notice in North East Somerset that it is sometimes convenient for farmers to go on roads on their quad bikes, so I would be reluctant to advocate a complete ban, but it is obviously important that all road users are safe."
Ms Cummins responded: "The people of Bradford deserve better than this, and I will continue to push the Government on this issue."
Previously West Yorkshire Police set up its own 'Quad Squad' to catch dangerous riders.
Since July 2014 they have seized more than 1,000 vehicles.
Last year The Yorkshire Post reported on a significant rise in quad bike theft in North Yorkshire where criminals target farmers and landowners, resulting in huge and often devastating financial losses.
North Yorkshire Police figures obtained by this newspaper showed the force recorded 103 thefts, or attempted thefts, of quad bikes between April 2019 and 2020.
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