Aristocrat Rhodri Phillips, who is the the 4th Viscount St Davids, was sentenced to 12 weeks in prison after posting threatening and racist messages about Gina Miller.
Ms Miller had brought a case to the High Court that argued MPs needed to vote on whether Britain triggered Article 50.
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Just after that case was successful, he wrote online: "£5,000 for the first person to 'accidentally' run over this bloody troublesome first generation immigrant."
Philipps, of Knightsbridge, central London, described her as a "boat jumper", and added: "If this is what we should expect from immigrants, send them back to their stinking jungles."
He was convicted at London's Westminster Magistrates' Court of two counts of sending menacing messages on a public electronic communications network.
The other post Philipps was convicted for was in response to a news article about an immigrant and his children.
As well as being the 4th Viscount St Davids, Philipps has a range of titles, also including Lord Hungerford, Lord de Moleyns, and Lord Strange of Knockin.
Ms Miller has revealed that her life was completely changed by being part of the case, and that she receives repeated threats for having funded it. She has been forced to hire her own security team, and does not take public transport or leave the house at the weekend.
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