Answer: Macduff travels to england because he does not agree with Macbeth's rule/leadership. He looks for supporters to help to overthrow him and get a new leader.
Why does Macduff travel to England?

Lord Macduff the Thane of Fife is a character in William Shakespeare's Macbeth (c.1603–1607) that is loosely based on history. Macduff a legendary hero plays a pivotal role in the play: he suspects Macbeth of regicide and eventually kills Macbeth in the final act. He can be seen as the avenging hero who helps save Scotland from Macbeth's tyranny in the play. The character is first known from Chronica Gentis Scotorum (late 14th century) and Orygynale Cronykil o…

Shakespeare's source for the story is the account of Macbeth King of Scotland Macduff and Duncan in Holinshed's Chronicles (1587) a history of England Scotland and Ireland familiar to Shakespeare and his contemporaries although the events in the play differ extensively from the history of the real Macbeth.

Macduff's son - Wikipedia

Macbeth then enters and they congratulate him on his victory. He later appears in Macbeth's castle as a guest. When his father is killed he is suspected of the murder so he escapes to England. He later makes an appearance in Act 4.3 where he talks to Macduff about Macbeth and what to do. They both decide to start a war against him.

Gently informs MacDuff that he is a suspect in the death...

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