I left the UK 3 years ago and went non-resident, just filled out the P85 and got a letter back fairly quickly saying something like "you are now considered non-resident for UK tax purposes".
I might have included a photocopy of the air ticket with the form, don't think so though, although I did use this to amicably cancel all contracts such as gym membership, TV license (refunded), mobile phone, broadband. I was expecting to have to pay these out, but once I mentioned I was leaving the UK indefinitely they said it was a justifiable cause to cancel it and did so without penalty. Actually virgin gym tried to tell me even after years, the contract auto renewed for 12 months and was not month by month - had to break that by saying they were in breach of the contract I originally signed as they had replaced some machines with alternative/functional models.
Of course property or a wife/child left behind would most probably complicate being "granted" non residency. I was self-employed before leaving, so to finalise some returns/refunds they owed me since leaving, gave my new Argentine address which is where they now send the letters, and have had them pay me into my UK bank account which I kept (along with credit cards). Have to do a return too for a UK partnership each year which hasn't caused any issues either (although tax is due on this as it is UK earnings). With a UK bank you can also fill some form if not uk tax payer to make sure the tax isn't applied to any interest payments.
My status in Argentina is still "tourist" (90 day visa entries). Unlike other stricter countries like Brazil that limit you to X months in a rolling 12 month period, most people just cross a border to reload the 90 days. Last time I left I was about 6 months over the 90 days and just had to pay a £50 fine before leaving Argentina. After 2 years of "living" in Argentina you are entitled to citizenship - they even accept as a means of "earning an honest living" as working "en negro" (not registered/paying tax). Haven't done it myself - its a plan B if the border hopping becomes non-feasible - not that this thread was anything to do with Argentina...