A look at Twitter also reveals a catalog of racist and sexist abuse against Miller, whose legal action thwarted the UK government's plans to trigger Article 50 of the Lisbon Treaty -- starting the formal process of Britain leaving the European Union -- without a vote in Parliament.
Miller, an investment banker who was born in Guyana but has lived in the UK for 41 years, told BBC Radio 5 live she planned to report the trolls to police, and that others had already done so.
She said other abuse included people telling her, "I'm not even human, I'm a primate, I belong in a kitchen -- that's the nicest of some of them. It is unbelievable.
"I am really cross at the politicians and the media who are whipping this up because they are the ones inciting racism and violence and acrimony."
Asked about the online abuse directed toward Miller, London's Metropolitan Police Service said it was aware of the issue.
"Police are aware of threats made on social media made towards an individual. The threats were made on 3 November onwards," a spokesman said. "Officers are in the process of contacting the individual involved."
Britain has been embroiled in a rancorous debate since the High Court ruling Thursday.
Reflecting wide unease about such criticism of the judiciary, the Bar Council, which represents all barristers in England and Wales, on Saturday condemned "the serious and unjustified attacks on the judiciary" seen since the ruling and called on the government to do so, too.
Liz Truss, who as UK justice secretary and lord chancellor is responsible for the courts and constitutional affairs, later issued a short statement.
"The independence of the judiciary is the foundation upon which our rule of law is built and our judiciary is rightly respected the world over for its independence and impartiality," she said.
"In relation to the case heard in the High Court the Government has made it clear it will appeal to the Supreme Court. Legal process must be followed."
'Send her some love'
The insults and worse coming Miller's way have also prompted an outpouring of support online.
Diane Abbott, a member of Parliament for a London constituency, described the abuse as "sadly predictable" on her Twitter feed.
And The 3 Million, a grass-roots campaign group run "by EU citizens for EU citizens" in Britain, urged its Twitter followers to show their backing for Miller.
Another pro-Europe campaign group, Britain for Europe, called for people to thank Miller and "send her some love."
The government said it remains committed to invoking Article 50 by the end of March. The Supreme Court is likely to hear its appeal against the High Court ruling in early December.
If the appeal fails, the process of leaving the EU is likely to be slowed down significantly while a Brexit bill is drawn up and then debated in the House of Commons and the House of Lords.