To expand on my remarks above, I think its important to consider the entire situation that Elizabeth and England found themselves in.
Lets remember that Elizabeth succeeded her half-sister Mary. Mary achieved an amazing though short lived thing: the recovery of England to the Catholic Church. However, she did make mistakes. One of the bigger ones was her tying England to the Habsburg dynasty and to Catholic Spain.
One can understand why Mary did this. Historian Diarmaid MacCulloch writes that one of the reasons Mary was so bent on marrying a Catholic and producing a Catholic heir was that it was widely known that Elizabeth was Protestant. If Mary died without children, England would once again be lost to the Catholic Church. But her choice of a husband, the Habsburg Philip of Spain, was a bad move in the long run. It was not popular in England since the English did not like thinking that they might be swallowed into the Habsburg Empire (and the Protestants certainly did not want to think of the prospect of their kingdom being tied to the very Catholic Spain). But she got her marriage, with some restrictions (such as Philip not getting to inherit the kingdom if Mary died without an heir).
She also got reunion with Rome in 1554, but the nobility and the gentry were not particularly excited about it. After being free of papal legal authority and enjoying the wealth generated by confiscated church lands, they didn’t really get any advantages out of the bargain. It was only when these landowners were secured in their acquired property that reconciliation could occur.
These were two important victories, but then she made mistakes. One was the decision to try Archbishop Cranmer for heresy. She could have just executed him for treason due to his involvement in the plot to make Jane Grey queen. Instead, Mary was embarrassed when Cranmer recanted his recantations! and died a dramatic death as a Protestant martyr.
She made matters worse with the reintroduction of medieval heresy laws after 1555. In only 4 years, 300 people died, burned for heresy. And of course, these Protestants became martyrs, which only gave the Protestant cause moral credibility and made the Catholic restoration turn sour for a lot of Englishmen. It also gave Protestants propaganda, such as
Foxe’s Book of Martyrs which set the Catholic cause back.
All of this, by the way, was made worse by papal politics. Pope Julius III had sent Cardinal Pole to England in November 1554 with legatine powers to reconstruct Catholicism, and he was doing a pretty good job before he died in 1558. But only 6 months after England reconciled with Rome, Paul IV became pope. He removed Pole as his legate and summoned him back to Rome to be tried for heresy. The very Catholic Queen Mary

protected Pole and allowed him to continue his efforts at restoring Catholicism.
Paul IV, along with France, declared war on Mary’s husband. This war led to England’s loss of Calais, its last French possession. In the last year of Mary’s life, she had to face stomach cancer, humiliation over losing Calais, and had to defy the Pope in order to keep her Archbishop of Canterbury.
In any event, Mary died. Elizabeth was raised Protestant. Everyone knew she was a Protestant (though she was smart enough to keep her head down and out of trouble during Mary’s reign). The fact that she was a convinced Protestant is obvious in that she went trough the trouble of undoing all of Mary’s work. While there was Protestant sentiment in England, the truth is that England was horribly polarized between Catholics and Protestants.
If she were truly a Catholic, she could have fought for a Catholic regime. She did not, which obviously indicates that she truly held Protestant beliefs.
That being said, she was lucky. At the time of her accession, elections to the House of Commons produced a majority prepared to back Protestantism. So, there was at least enough support in England at the time to make a Protestant regime a viable option. That viability and Elizabeth’s natural sympathy toward the Reformed faith informed her political decisions.