Ok, here's a quick thing to show how this may come about:
1502: Arthur Tudor, Prince of Wales dies. His bride, Catherine of Aragon, is discovered to be pregnant.
1503: Catherine of Aragon gives birth to Henry Tudor, who is made the Prince of Wales.
1509: Henry VII dies and the Prince of Wales ascends to Henry VIII, under the regency council, including his uncle, Henry Tudor, Duke of York.
1510: The betrothal between the Prince of Wales and Isabella of Austria is finalized. Henry Tudor, Duke of York marries Philiberta of Savoy, who is 12.
1513: Henry Tudor, Duke of York, welcomes his first child, Mary Tudor of York.
1516: Isabella of Austria arrives in England, to be married to Henry VIII of England. Henry Tudor, Duke of York, welcomes his second child, named Henry Tudor of York.
1517: Henry VIII welcomes his first child, named Catherine Tudor.
1518: Henry VIII welcomes his second child, named Arthur Tudor.
1520: Henry VIII welcomes his third child, named Margaret Tudor.
1522: Isabella of Austria, Queen of England, dies giving birth to twin boys, who die soon after the birth.
1523: There is scandal in the court as the King, now 20, announces he has married English noblewoman Anne Boleyn, the younger daughter of noted diplomat Thomas Boleyn. The union had been rumoured at, but only in the sense she was his mistress. However, they have all of their papers in order and Anne Boleyn is crown as Queen of England. There is animosity between the Princess Dowager and the young woman, who Catherine feels destroyed her son's chances at continuing the alliance with her family.
. I figure the most likely way to do this would be to have Catherine either have a son with Arthur, or to marry Henry ASAP (though the bottom end of the spectrum for Anne Boleyn's birth is around 1507, so a little wiggle-room I guess).
