In 1628, fed up with the behaviour of King Charles I, the English parliament instituted the Petition of Right, which limited the power of the King to tax without going through parliament, to enact martial law, and from an individual rights point of view, it stopped him (and thus the government generally) from imprisoning people without cause, or forcibly billeting soldiers in their house. These were, according to parliament, essentially restating rights guarenteed by the Magna Carta. Of course, Charles was not very happy about this, and relations between King and Parliament worsened until eventually leading to Civil War.
60 years later, Charles's son James II, similarly accused of tyranny (and worse, Catholicism!) was overthrown by his daughter and son-in-law, at the urging of Parliament, in what became known as the Glorious Revolution. Of course, Parliament was not keen on perhaps one day facing yet another tyrannical King, and so in 1689 King William and Queen Mary signed a very important document: the Bill of Rights. (Yes, that's where the American document got its name.)
The English Bill of Rights guarenteed the following: laws should not be dispensed with or suspended without the consent of Parliament; no taxes should be levied without the authority of Parliament; the right to petition the monarch should be without fear of retribution; no standing army may be maintained during peacetime without the consent of Parliament; subjects who are Protestants may bear arms for their defence as permitted by law; the election of members of Parliament should be free; the freedom of speech and debates or proceedings in Parliament should not to be impeached or questioned in any court or place out of Parliament; excessive bail should not be required, nor excessive fines imposed, nor cruel and unusual punishment inflicted; jurors should be duly impannelled and returned and jurors in high treason trials should be freeholders; promises of fines or forfeitures before conviction are void; Parliaments should be held frequently
It should be noted that the document claimed not to be inventing these rights, but rather reasserting "ancient rights and liberties". As far as they were concerned, this all goes back to the Magna Carta, though that's not completely accurate (nor does it have no truth to it).
Now, you might note that, from an individual point of view, the Bill of Rights didn't actually guarentee that much. It gives, for example, Parliament the right to freedom of speech, but not individuals.
It does, however, guarentee some individual rights, relating to criminal prosecutions (for example, no cruel or unusual punishment: previous to this, torture hadn't been allowed either most of the time, but it could happen with the King's permission, rarely but occasionally given. This stripped the right of the King to order torture.)
I'd like to leave someone else to go into what natural rights the Magna Carta actually guarentees, however. It's important to note that many of the rights in the Magna Carta only applied to free men (a minority of the population at the time). For example: "No freeman shall be taken or imprisoned or disseised or exiled or in any way destroyed, nor will we go upon him nor will we send upon him except upon the lawful judgement of his peers or the law of the land." (Though I assume the American Bill of Rights didn't apply to slaves either? I don't actually know. I remember something about slaves being worth 3/5 of a Freeman?)
The Bill of Rights 1689 on the other hand, says nothing about applying only to Freemen (though you'll notice that only Protestants were guarenteed the right to bear arms, not Catholics), and thus applied to everyone in England.*
*Slavery was never actually banned in England, it was retroactively judged illegal in court cases during the 18th century. Since there was no law saying slaves existed, the court decided they were therefore not slaves, thus it was illegal to kidnap them and force them to work. Of course, for 100 years slave-owners conveniently ignored this, until abolitionists found a judge sympathetic to their claims and a convenient legal case (a slave who'd been brought to England, escaped, and recaptured by his master) to try it under.
If you want, I can give you a description of the Greek political system, if that interests you.