First of all she did not become Queen of England but became Queen of the United Kingdom of Great Britain and Ireland, the Kingdom of England had ceased to exist with the 1707 Acts of Union which united the Kingdoms of England and Scotland into one Kingdom of Great Britian (The seperate Kingdom of Ireland was merged with the Kingdom of Great Britian in 1800)

And as for William IV's children; they were all illegitimate, born to his various mistresses and therefore not eligable to inherit the throne.

Inheritence to the British throne did not exclude females but was male preference, meaning that if a monarch had say two legitimate children, the eldest a female and the youngest male the son would be in line before the daughter.

The more interesting question is how Victoria inherited when he grandfather George III had quite a few legitimate children and Victoria's father Edward was only his foruth child?

George III had quite a large family and a number of sons. The inheritence as I mentioned earlier was male preference so the males came first in the order of succession, George the Prince Regent was his eldest and thus next in line. He was married and had one child, a daughter Princess Charlotte. As the only child she was his heir, so she was second in line to the throne.

So the succession seemed safe, George would inherit the throne and then upon his death Charlotte would become Queen. But Charlotte died in 1817 giving birth to her stillborn son. What of the succession now?

George III had a number of children, after George the Prince Regent there was Frederick who had married Princess Frederica Charlotte of Prussia in 1791 but they had no children. Prince William was the next eldest child of George III, he was unmarried but had a number of children with his mistress Dorothea Jordan (as his elder brother already had a child it seemed the succession was secure so why bother getting married and settling down when he could live it up with a mistress?). As they were unmarried their children were illigitimate bastards and thus could not inherit the throne. Next up was Charlotte the Princess Royal who was placed behind her brothers, both elder and younger in the line of succession due to the aformentioned male preference inheritence. She was married but also had no children. Then there was Prince Edward who was unmarried. And then there was a number more sons and daughters, some were married and some were not but it's not of great importance to Victoria's eventual inheritence so I'll skip over them.

When Charlotte, the daughter of the Prince Regent died there was a bit of a sucession crisis as there were no other legitimate grandchildren of George III. There was a lot of pressure upon the King's other unmarried sons to get married to produce more heirs to the throne. William married Princess Adelaide of Saxe-Meiningen in 1818 and Edward married Princess Victoria of Saxe-Coburg-Saalfeld also in 1818. In 1819 Edward and Victoria had a child, Alexandrina Victoria the future Queen Victoria)

So now the succession went: George the Prince Regent, Frederick, William and Prince Edward. Then as his only child Victoria was next, fifth in line. And then the other children and grandchildren of George III but we're ignoring them to simplify things a bit.

George III died in 1820 and The Prince Regent inherited the throne as George IV. His wife, Caroline of Brunswick died in 1821 and the King never remarried and so had no further children.

So now the line of succession went: 1-Frederick, 2-William, 3-Edward, and 4-Victoria (5,6,7, etc)

Prince Edward died in 1820 leaving Victoria as his only child.

1-Frederick, 2-William, 3-Victoria

Prince Frederick died in 1827 without any children

1-William, 2- Victoria

George IV died in 1830 and William became William IV.

1- Victoria

William IV died in 1837 without producing any legitimate children with his wife Adelaide, and none of his illigitimate children could inherit so Alexandrina Victoria became Queen Victoria.

And that's how Victoria managed to become Queen of the United Kingdom despite being the only child of the fourth son of George III.

A few years back the inheritence laws were changed in the UK and the 15 other Commonwealth Realms so that there is no longer any male preference, males and females are both fully equal when it comes to the line of succession.

And a bonus round: George III was not only king of Great Britain but he was also King of Hannover in Germany (why? that's another question relating to the 1701 Act of Settlement). The Kingdom of Hannover had different succession laws, it excluded females from inheriting at all. So after the death of Wiliam IV Victoria could not inherit the Kingdom of Hannover and it went to her uncle Ernest Augustus who became King of Hannover in 1837 as the eldest legitimate male heir to the throne.