The comments come after white supremacist Thomas Mair was jailed for life for murdering Labour MP Jo Cox.
The 41-year-old politician was shot and stabbed to death by the 53-year-old loner last June in Birstall, West Yorkshire.
Speaking to The Evidence-based Investor about the backlash to the Article 50 ruling, Ms Miller said: “Some people have said, you know ‘you get keyboard warriors’ [but] this is on a different scale to that.
“This is very personal, there”s been phone calls, emails, my office has been bombarded with the most hateful messages and calls, death threats – I am under police protection.”
The campaigner said she did not expect the level of abuse targeted at her after she won the battle to ensure Article 50 is triggered through a parliamentary vote.
She said: “It has gotten to a stage where I”ve seen a very dark side of society and I have to say, I think those dark forces were always there but they”ve now somehow emboldened and been legitimised.
“Unfortunately to come out of the dark corners and to believe that they can go out and threaten me with rape, death, whatever you name [it] – beheading.
“And unfortunately we”ve just seen the Jo Cox trial and that has emboldened another faction who believe that I should be Jo Cox number two, there”s even a bounty on my head for £5,000 to run me over. It is extraordinary, I never expected the level of sexual and racial violence that I”m experiencing.”
The social media call was one of a number of threats Ms Miller has received since the High Court ruling, which is now being appealed by the Government in the Supreme Court.
The comments from the investment manager, who called on politicians do more about it, come after she revealed she spent thousands ramping up her personal security.
She said: “There is a security burden that I had not envisaged. I have had to take measures for myself and my staff as well as for the business and website — all in all, we”re talking £50,000-£60,000.
“It may be more, depending on what happens at the Supreme Court.”