Yeah, I did it. My application for permanent residence is now in hand.
I just have to wait 30 days for approval; I do not anticipate any issues along the way.
A bonus of having permanent residence in one country in the EU is that it can be exchanged for residence in any other EU country with minimal fuss.
The rules for residence vary across the EU; however, Britons would have several routes that would lead to residency. For example, in Estonia, one can obtain residence on the basis of existing income (which is not too high).
A visa is required if a person from outside the EU wants to spend an extended period in the EU. There are all sorts of these, and they vary from country to country. But it isn't too difficult to get one, as long as one is solvent and not from a 'troublesome' country.
Once one has EU residence, one can spend extended periods in all the countries of the EU. So, Spain is a nice destination; it is where I spend a chunk of time. I obtained an NIE which is a non-resident bit of paper that registers one as a person in Spain, enabling one to have bank accounts, buy property, interact with officialdom, etc.