Did Orlando Bloom try for a part in Eastenders?

Yes - but Orlando Bloom was delighted that they turned him down and inadvertently launched his Hollywood movie career.
He was due to play Pat Evans' long-lost son four years ago, but was rescued when the producers changed the storyline and removed his character.

He possibly could have played a toy seller in the market that ran out of toy bricks and was Lego less.

[Jul 06 04 4:35 PM] Senior Moments writes:

He appeared in Midsomer Murders playing Peter Drinkwater in an episode called "Judgement Day"

He was a casualty in Casualty once. Never been in The Bill though. Unlike the rest of the acting profession.