Suggestion : We voted to withdraw the UK from the EU (Brexit) as we believe it's important for the UK to be economically independent and to rely less on the the EU's

We voted to quit the European Union as we believe it is important to draw a line with European Union economic dependence and to have economic independence in the UK. Instead of "draw a line" I would choose something else. It's fine but maybe "withdraw" would be better. Remeber "Brexit" means "British Exit" and is a noun.