They left because the wanted freedom snd they could not survive without the main source of food a.k.a. The potatoes and tomatoes
At the time, England made it much easier for the Irish to migrate to the USA and Canada, realizing it would be cheaper for them than keeping the starving Irish there. They often paid them measly amounts to leave their homes, then offered them an 'generous' boat ride to America. Many died on these ships from malnutrition and disease, earning them the nickname 'Coffin Ships'. Actually, surprising numbers of people might have outlasted the famine had the British not discriminated against them so greatly, exampled by evicting them from their houses, raising their rents, and forcing them out of British cities and towns to go back to their home isle.
Many people were dying from starvation because they couldn't eat the potatoes and that was their main source of food. They had to move out of Ireland so they would outlive the famine.
They came to England because England is very close to Ireland, so it would be easier for them to get to.