Brexit & Royal Assent

As most of the world is aware by now, the United Kingdom voted in June to exit from the European Union.

While the vote is guidance for Parliament, the actual act of exiting the European Union (by invoking Article 50 of the Lisbon Treaty) formally has not started by the House of Commons.

I wonder if Parliament passes a bill "activating" Article 50 by petitioning the European Council, what measures could be taken inside the UK to prevent the formal exit request?

In 1707, Queen Anne was the last British monarch to refuse royal assent to a bill of Parliament. Accordingly, the monarch has the constitutional authority to refuse royal assent (veto). By this way, could Queen Elizabeth II save her nation from potentially losing Scotland and Northern Ireland?