In a scathing attack, she vowed to introduce primary legislation to restrict the human rights of offenders after a minority of the judiciary decided to "ignore parliament's wishes".
But she warned the delay in getting that on to the statute book would inevitably mean "more victims of violent crimes committed by foreigners in this country".
MPs approved new guidance for judges in July last year making clear the right to a family life - set out in Article 8 of the European Convention on Human Rights - was only qualified.
The change was designed to end a string of cases where it was used to justify granting foreign criminals the right to remain in the UK rather than being deported.
Labour questioned at the time whether the guidance would be sufficient to override the precedent set by earlier cases and said it would support primary legislation.
Last year, Conservative MP Charlie Elphicke obtained Home Office figures suggesting that 177 foreign criminals avoided deportation in the year 2011 to 2012 after convincing judges of their right to a family life in Britain.
They include Vladimir Buchak, a Ukrainian who paid eastern Europeans with the right to live in Britain up to £3,000 to marry Africans. He has been allowed to remain because he has two children here.
A Jamaican drug dealer was allowed to stay in the UK with his family after his release, after the High Court cited the effect his absence would have on his nine-year-old son who suffers from ADHD.
And Aso Mohammed Ibrahim, an Iraqi Kurd, killed a 12-year-old girl in a hit-and-run in Lancashire, and was allowed to remain in the UK after his release from four months in jail, because of his family.
She said: "Unfortunately, some judges evidently do not regard a debate in Parliament on new immigration rules, followed by the unanimous adoption of those rules, as evidence that Parliament actually wants to see those new rules implemented," she wrote.
One judge, she noted, had justified his decision on the basis that the new guidance had been subject only to "a weak form of parliamentary scrutiny".
"It is essential to democracy that the elected representatives of the people make the laws that govern this country - and not the judges," she wrote.
"Yet some judges seem to believe that they can ignore Parliament's wishes if they think that the procedures for parliamentary scrutiny have been 'weak'.
"That appears actually to mean that they can ignore Parliament when they think it came to the wrong conclusion."
She said she was determined to bring forward a new law making it clear the deportation should be the norm in everything but "extraordinary circumstances".
"It is depressing that the steps we have already taken should have been insufficient to produce that result.
"The inevitable delays inherent in passing primary legislation will mean that there will be many more foreign criminals who successfully avoid deportation on the basis that they have a family here.
"There will also be more victims of violent crimes committed by foreigners in this country - foreigners who should have been, and could have been, deported," she added.
Judges who allowed prisoners to remain were also guilty of reinforcing public perceptions of human right as "legal dodges that allow criminals to escape proper punishment and to continue to prey on the public.
"This is not a dispute about respect for human rights, which I certainly agree is an essential part of any decent legal system.
"It is about how to balance rights against each other: in particular, the individual's right to family life, the right of the individual to be free from violent crime, and the right of society to protect itself against foreign criminals."
May insisted that she was "a great admirer of most of the judges in Britain" and accepted the need for the power of government ministers to be "reviewed and restrained" by the judiciary.
"But the law in this country is made by the elected representatives of the people in Parliament. And our democracy is subverted when judges decide to take on that role for themselves."
Business Secretary Vince Cable said legislation would undoubtedly be popular but cautioned against "second-guessing" judges.
"I am sure she is right that the public mood - and that is shown across the political spectrum - believes that if people have committed very, very serious offences in this country then they should be deported, if that's the appropriate penalty," the senior Liberal Democrat told the Murnaghan programme on Sky News.
"But we can't be in the business of second-guessing individual judges' decisions. We have an independent judiciary and we have got to respect that.
"But if she wishes to bring in measures to prevent serious abuse of the system by overseas criminals I'm sure that will be widely welcomed."
Work and Pensions Secretary Iain Duncan Smith told BBC1's Andrew Marr Show: "The truth is the judges know very well the mood and the mind of Parliament, but they've continued to trump that with this business of the right to a family life.
"Parliament made it very clear previously - under previous legislation and the guidance particularly - that they wanted to know that if a criminal commits a crime, then they should be in a much stronger position to be able to extradite them and kick them out if they came from overseas.
"And that's what she's saying today and that's what she is going to ensure again in further tightening up of the guidance."
Labour peer Baroness Kennedy, a human rights lawyer, criticised Mrs May's attack.
"This depresses me. It's a common story with home secretaries that this is what they end up doing," she said.
"We've got to remember that this is about the independence of the judiciary and why that's so important.
"It's absolutely imperative that judges are not under the thumb of home secretaries, and it can be frustrating for home secretaries of course, but it is not good to see this kind of vocal attack on the judges, and I am sad that she has done this."