Nesting Magpies

I have discovered nesting magpies in a large tree which I plan on removing from the garden. As I understand it Magpie chicks are laid in April and require 4 weeks before fledging and a further 4 weeks being fed by their parents meaning they would be gone after 2 months making it safe for me to remove the tree from July. Please advise if this is correct so I can remove the tree legally.