The Euro is not a requirement (obviously) of being in the EU. If the sovereign UK or sovereign Ukraine or sovereign Sweden (or Norway, or wherever) want to acquire/retain EU membership but don't want to adopt the Euro, then that's absolutely their right.
The EU is a wonderful (and of course imperfect) organisation because it is democratic, because it's a voluntary association of democratic states. Yes, being a member has some basic requirements (like upholding rule of law), but let's not pretend it has to be all or nothing.
The UK will I suspect one day rejoin the EU, and when it does, it will be two mature political entities coming to a mutually beneficial agreement.