It is worth a few minutes looking through the HMRC guidance
I think it would be wise to look at the Schengen Visa
These are a few links (when searching for Schengen Visa watch out for scam sites) explaining the Schengen visa for BRITS who will become third country nationals after Brexit.
Calculate your stays if you have a Schengen Visa.
This handy tool will help you.
http://schengen-calculator.com
Or this one http://adambard.github.io/schengencalc/
and this for background
All the EU visas
In addition the ETIAS (the Schengen version of the USA ESTA) will add a further layer of control to those crossing the Schengen border.
This site explains ETIAS and how it will work in 2021/2022
(When searching for ETIAS watch out for scam sites) It is searchable so a British or any Citizen can check what is thought will be needed after Brexit.
Applications will be made online and there will be just the same issues that people have had with America, ie overstaying your Schengen/long stay Visa may result in being refused re-entry.
Thank you very much for all of these Graham, much appreciated.
After your warning about scam ETIAS websites it might be worth reading the disclaimer at the foot of the page of the site that you linked to 
DISCLAIMER STATEMENT
EtiasEurope.eu is a private Website tha provides the latest News and Information regarding travel to the Schengen area and information about the new European Commission’s legislative proposal for an EU Travel and Information Authorisation System (ETIAS) . Because of the nature of this topic and the continuous updates of the legislative initiative, we strongly suggest that all visitors get the latest updates on the official EU governative websites
Which takes us back to where we started! As in post 2, a Visa D!!
As I said before there are a range of visa available for non-europeans. Some, like student visas, are for set terms and don’t make you a tax resident. But as far as I can work out the only visa available to someone in Adrian’s position post January is the visa D. Which does open you to become fiscally resident here.
Nigel, I am aware. However as with all things even non official sites can provide information.
The “scam” is likely when ETIAS becomes live and people will be charged a “processing fee” just like so many sites do fo ESTA, passports etc etc.
Millions are made by these people and rarely does the official site come top of the list on Google.
There doesn’t appear to be any official ETIAS site yet so all those that are found are just speculating.
It will be an .eu site
Anyone resident in the EU (including the UK until 31st December 2020) can have a .eu website. There is no official EU domain like .gouv.fr or .gov.uk
I apologise. You are absolutely correct. europa.eu it is I should have clocked this from the many bookmarked pages I have for EU directives & other official EU documents.
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