West Yorkshire Police Roads Policing Unit said the vehicle which crashed was believed to have no insurance.
Then a second private hire taxi which arrived at the scene was suspected of being un-taxed.
The tweeted a photograph of both vehicles strapped to the back of wagons on Bowling Back Lane, Bradford, before they were removed from the scene.
They said: "First private hire vehicle crashes into a wall, believed uninsured and no tax. Vehicle seized. Second private hire vehicle arrives to collect the first driver, also not taxed and also seized. Awaiting third vehicle."