Short answer: They used to be called Tories, and changed their name to Conservative.

Long answer:

To understand the full context, you need to understand a bit about the development of the Conservative party, and parliamentary politics itself.

In the English Civil War, there were two sides: supporters of the monarchy, and supporters of parliament. Although this war was primarily about whether the King or Parliament was supreme, there was a lot of religious influence mixed in. Charles I, while a Protestant, was one whose preference in religion was rather Catholic-esque. One of the triggers of the civil war was his introduction of a liturgical prayer book in Scotland, which many Scottish radical protestants hated. These Scottish "covenenters" joined with supporters of Parliament, many of whom (including Cromwell) were Puritans (another form of radical protestantism that was violently opposed to Catholicism). Meanwhile, most of those who wanted England's Church to be less radically Protestant, and more similar to the Catholic Church (although without the Pope), fought for King Charles. And of course, so did actual Catholics, like the Irish.

So, we've got Irish and Anglo-Catholics on one side, and Scottish covenenters and puritans on the other side.

Now, fast-forward through the rise and fall of republicanism in Britain, to King Charles II. He dies without children, leaving the throne to his Catholic brother, James II. Some politicians support him (he is, after all, the legitimate heir). Others oppose him, because he's a Catholic. Both sides throw insults at each other. His supporters get called "Tories" meaning Irish outlaws. Why? Because it goes back to the supporters of Charles I, who had the support of the Irish. Meanwhile, those who oppose him get called "Whigs", meaning Scottish cattle-drovers. Why? It goes back to the opponents of Charles I, who had the support of the Scottish covenanters.

Now, James inherited the throne, so the Tories were in ascendancy, but later he was chased out by his daughter and her Dutch husband and his army (at the invitation of Whig politicians). However, in return for the throne, the new King William and Queen Mary agreed to give up various powers in the Bill of Rights, 1689. Some Tories continued supporting James and his son, and so were seen as traitors, and lost power for a while.

Of course, over the next century, politics changed a lot. But the names stuck around.

Those who supported the rights of the monarchy, and the ascendency of the high Anglican Church, with its bishops and arch-bishops, were known as Tories (ironically, these were actually more anti-Irish and anti-Catholic). Meanwhile, those who wanted the monarchy to be further stripped of its powers, and who wanted more freedom for radical Protestants (like Quakers, Baptists, and later Methodists), were known as Whigs. They also even wanted slightly less harsh restrictions on Catholics and Jews, as a general support for religious liberty. (The Whigs were actually sort of descended from the 17th century Tories, but it's a bit complicated and doesn't really matter.)

It should be noted that these were general terms: there was no official party system, and MPs were not registered as being officially "Whigs" or "Tories".

As the 19th century began, two big new issues arose. Firstly, only the rich could vote, but the poor and middle-class were demanding the vote. People at the top were worried about a French-style revolution, and the atrocities of the Terror were in their minds. The two parties took different views: the Tories wanted to resist giving out the vote, while the Whigs thought that by giving the middle-class the vote, they would divide and conquer, and so not have to give the poor the vote. The second big issue was protectionism vs free trade. Generally speaking, the Tories were anti-free trade, while the Whigs were pro-free trade (though it's a little more complicated than this).

In 1832, the Whigs passed the Great Reform Act, which cleaned up many of the corrupt and unrepresentative boroughs (constituencies) of Britain, making it fairer, and also gave many middle-class people the vote.

This of course, was a big blow for the Tories. But a charismatic young Tory, Robert Peel (inventor of the police in Britain: that's why we call them bobbies), a former Home Secretary, was asked by the King to be Prime Minister in 1834. He reorganised the party, releasing a manifesto (in which he accepted the Reform Act), creating a central strategy, and getting people to canvas in support of the party. Essentially, he began the process of turning them into a modern party. He therefore needed a proper name: the name chosen was Conservative, a term that had been going around for the last few years.

Peel later lost power, as he was extremely unpopular with other MPs in his party (he wasn't from as rich a background as them, and he supported free trade, while most Conservatives supported protectionism), but the name stuck.

Because of that, some of his strongest supporters, led by William Gladstone, left the Conservative party. They ended up voting alongside the Whigs, and radical MPs (mostly non-Anglican protestants who wanted what we'd see as more leftist politics, though that wasn't really a term used in Britain at the time), and in the end together formed the Liberal Party (ancestors of today's Liberal Democrats).