Why did many in the south believe that britain would support their cause ? why britain remain neutral ?

British were against Slavery.

Explanation:

In the middle of nineteenth century, a bulk of the world's cotton was produced within the “Southern States of America”. British did not need Southern cotton. After the crop failure they had to buy 'wheat' and 'corn' from the North. South used slaves as labors and also during wars. British opposed this.

Great Britain was divided throughout the civil war in opinions to support U.S. or not. The “aristocrats” and the “working class” of British society supported the South. “The Confederacy”. The lower class, factory workers, intellectuals supported the North. So, staying neutral was the best choice for the economy of Great Britain as it could trade with both the opposing sides of the war in that case.

this is a good question! i'll do some research and come back when i have the answer!