I do on-call for IT. We get a flat on-call rate, split between the team covering the rota. I think it's £12500 a year currently, split between 4 of us, and you get paid a 12th of your share each month. We are expected to respond within 15 minutes and if required, be on-site within 30 minutes. (There's more than one site, and we all live at least 40 minutes away from our closest because we all live close to the day office.
Most calls can be dealt with remotely, so this hasn't been an issue to date.)
We are expected to remain sober. We can travel if we can still be contactable and have access to log on remotely, so I can run the usual weekend errands, and I've been to a friend's party in the next town (I did have to log on during that one.) But I can't go and see my sister two hours away.
If we do more than half an hour of actual work, we can claim TOIL or overtime, but there's a preference for us to take time rather than money.
Our colleagues in the Netherlands (and how it worked in a previous job) was that you get a rate for each shift on call (overnight, or weekend/bank holiday day.) You got a payment for each call (around £5), and then they can claim for actual time worked. I prefer that way.
So for us, we are paid to be on-call, which compensates for our lives being restricted during an on-call week, and we get paid for actual work. There are occasionally bad shifts with a major outage, but hardware is much more resilient these days, and it's not like it was when I first started, and you could get several calls a night, and several bad shifts in a row.
I would definitely be complaining if I didn't feel I was fairly compensated for it, but currently, (shouldn't say this while I'm actually on-call,) we have it pretty easy these days. Obviously a completely different industry and type of duty, and therefore of limited use.
I agree that you are actually working and should be compensated. Also, as well as minimum wage, you should be allowed recovery time - we are allowed to go in late if we have a busy on-call shift. I think the working time directive says you should have 11 hours between shifts, but there could be some other wording to cover on-call, haven't read it in a while. If it's really that busy, it would make more sense to me to have someone cover it as an actual shift, but then they would have to pay an actual wage, not on-call rate.
If you're in a union, you should ask them.