Retain wage level in another country

This depends on the corporation. How they handle pay at other sites is an issue for them to address. In a large country even different regions of the same country have different costs of living.

That means that if they pay everybody with the same title and level in a narrow band, some people will financially struggle in their location, and others will live like royalty.

It gets even more complex when different countries have different tax issues, different required benefits, and different government programs. In some cases they provide additional funds to employees to address these issues. In some cases they don't. You will have to do some research to see what equivalent pay you will need to keep your standard of living in light of these differences.

It can also depend on how long the position is for. If it is viewed as a temporary assignment they may handle these issues differently. You might have to talk to somebody inside the company to see how the company handles these issues.

TL;DR: I want to move to the EU from the U.K. and keep the same pay (though not a Euro- using destination.) Is this possible?

Yes, it is. If you are self employed and your income is not depending on where you life - it is trivial. You move. You keep your income.

Assuming I can relocate is there any precedence for retaining the origin country/market pay scale/grade when an employee continues the same job but in a different country?

Yes. There is. Quite some. They all involve individuals that are "brands" and can not be replaced. I.e. Michael Schumacher went to Switzerland for tax reasons and it did not change his deal with Ferrari a cent.

If you are NOT a brand and your position is not one that hardly anyone can replace you in and that is absolutely critical for the company paying you - then... we all joke how stupid companies can be at times. You assume a new level of utterly stupid - basically you assume a company is too stupid to realize that by firing you and replacing you with someone else (locally) working for the local wages they can save a ton of money AND problems (when other people realize you get paid a lot more than them). This really is a new level of stupid to assume on a company (and man, in the last 30 years I do have seen some levels of stupid companies do, but then none of them came close to this).

So, no, the only 3 ways to keep your income when moving are:

• Your income is not dependent on your location.
• You are not replaceable and an SERIOUS asset of the company (i.e. the best driver on the planet for a racing team)
• The company sends you there. This mostly will mean a promotion - i.e. running a division for some years in another country), or it is i.e. an engineer overseeing a plant being built in another country - if this is time limited etc. it is not unusual to keep pay and add on top.

Any other case? You. Are. Replaceable. Why would they pay you way more than going market rate?

Also, you make a VERY fundamental mistake:

I’m living and working in the U.K. but want to move to an EU country.

Wage is not wage. I.e. in Germany your wage does not include all that is paid to you. Some things are split between you (in the wage) and the employer (ex wage, not part of the wage). This includes social security and retirement. Which means that while you get 100 (whatever unit) in the UK, you would get maybe 80 in germany, but on top of that another 20 would be paid by the employer for your benefit, but those are not seen as part of the wage (they are mandatory elements but not part of the number quoted). The tax situation may be totally utterly different. The COST side would be - especially if you come from the UK, ESPECIALLY the London area. You likely live in what would be illegal to rent out in most parts of europe (too small rooms) and pay utter insane rent (at least according to what I researched when I was considering taking london Contracts). There is more to standard of living (and even savings) than a pure number on a work contract.