@Voland's right hand Re: Complex problem
It is disappointing to see how credulous people can be, in believing (and transmitting) the nonsense published in the papers (the Daily Express, of all things), all in the name of protesting about Brexit. It's easy to see why the term "remoaner' was invented.
You, like many people, seem to be confusing what the EU requires with what it makes possible. Take driving licences:
There are mutual recognition agreements between them. This is the exact reason why UK license will NOT be recognized. There is NO mutual recognition agreement. It will be in the "yet to be signed" queue and (surprise, surprise) UK has not signed and ratified the relevant conventions to get an automatic recognition (at least Vienna convention of 1968, probably more).
Wrong. Mutual recognition is defined by international agreements that have much wider scope than the EU. The UK is one of the 74 signatories to the Vienna convention on Road Traffic of 1968, and has both signed and ratified its predecessor, the Geneva convention on Road Traffic 1949. Those conventions define mutual recognition of driving licences worldwide and will not be changed by Brexit.
Private drivers have the workaround of getting an international license so there is a way around it (albeit annoying and painful).
Wrong again. An International Driving Licence (or more correctly Permit) is merely an internationally-recognised translation of your national licence in an agreed format, as proof that you have a valid national licence. It's no "workaround", you still drive on your national licence, under the aforementioned agreements, which apply inside and outside the EU. You can get an IDP by post for £5.50.
The big Bugbear is the insurance. There is a mutual recognition agreement for 3rd party liability insurance in Europe which is beyond Eu. Non-Eu and non-EEA countries like Serbia, Monte Negro, etc participate in it and agree to the same final arbiter. That arbiter is the same as for Open Sky agreement. It is called ECJ. According to stated policy by UK government this is red line.
More FUD. International car insurance in Europe is covered by the Green Card scheme, which has 47 members inside and outside the EU, as you say it is not an EU system. The EU directives simply lay down the rules that EU members must follow in terms of having insurance, making claims etc. For example it makes having insurance mandatory (something that was not always the case, for example it's been mandatory in the UK since 1930, but only since 1958 in France). Here again everything exists without the EU, the EU just says how its members must apply the rules. Post-Brexit it would certainly be possible for, say, France to pass a law saying that UK insurance wasn't valid in France (or vice-versa). That would be a very stupid thing to do given the tourism that would be lost, and again it would need deliberate action. Bexit won't, in itself, change the current situation.
As for the ECJ, you are misrepresenting the situation. The UK's intention is to prevent the ECJ from being able to overrule UK courts on UK matters, the usual example being when a UK court decided to expel a hate-preacher and was prevented from doing so by an ECJ ruling that it would disadvantage his family. There's clearly no change in the ECJ's ability to rule on pan-European issues within its jurisdiction. The UK would still have to respect such judgements, just as it would respect US Supreme Court rulings on US issues, etc.
You're clutching at remoaner straws here. There are EU directives which require each EU member to enact national legislation on roadworthiness, Unless the EU or UK decides to change the rules in a non-compliant way this will remain valid. It won't magically evaporate after Brexit.
Clearly there will need to be agreement on data exchange rules, but that is so fundamental to all trade between EU and non-EU countries that it will obviously continue.
executive summary is - ROYALLY SCREWED
Not even close, but it's up to you. If you want to cower in your little English garden behind your little English fence, planning your next holiday in Skegness because you're scared the big, bad, Brexit wolf won't let you go anywhere else you are entirely free to believe that.
The rest of us will continue our travels around the EU, and the other 80% of the world, as before.