I'm sorry but there are a couple of questions in this one! I have decided to move permanently to another country in the EU. Is it a requirement that I inform the UK Government or is it okay to leave without doing so? I have arranged paying social security in my new country of residence, do I still need to social security payments in the UK? When it comes time for renewing my passport, am I going to be able to do that without having a permanent British address? Will be able, for example, to use my Nan's address in the UK?
You do not need a UK address to renew your passport, I am currently in the throes of renewing mine and have just filled in the forms so I would have noticed if I need a UK address.
You don't need to inform the government but you do need to get your tax sorted out and deal with the health insurance side of things. If you are going to live in France my experiences may help.