I have joined a new NHS department where it is deemed standard to be given annual leave and then to be rotared for out of hours shifts and residential on calls over this period. Managers then tell the employee that they will need to get these shifts covered. So staff are regularly rotared on-calls mid-annual leave or weekend shifts that they then have to sort themselves.
I have found that residential on-calls class as working time even when not actively working but I can't seem to find anything regarding the legalities of who's responsibility organising cover belongs to. My union have said that it is "unacceptable" but doesn't say what regulations it is unacceptable by and they aren't the most reliable of sources.
There's no locale stated, but normally responsibility lies at a different level from the actual employee. Whether that be the union, the employer, or both is dependent on locale, but unless it's in your contract somewhere that you're responsible for it then it's not you.
If you have a union, ask them. That's theoretically part of what they exist for.
It’s up to HR to find or not find a replacement for you. It may be that if you want to take some time off, you would need permission and you will only get it if you find a replacement, but once your holiday request has been accepted, it is up to HR.