On-call rota
An on-call rota is the plan of who can be called in, on which night or weekend. Being on the list is not the same as being at work. Minimum-wage hours and working-time hours are different questions, and a sleep-in is a third case with its own rule.
Minimum wage: where they are waiting
GOV.UK’s guidance on hours that count for the minimum wage says time on standby or on-call at or near the workplace usually counts. Time spent at home, waiting to be called in, does not. They become entitled for the hours after they have arrived and are working or available for work. Travelling from home to a call is not, on that guidance, automatically time the minimum wage must cover. Pay for the inconvenience of carrying the phone can still be in the contract. That allowance is not a substitute for the rate on the hours that do count.
A sleep-in is narrower. The person is required to be at or near the workplace, is expected to sleep for most of the shift, and is woken if there is a task. Where suitable sleeping facilities are provided, the minimum wage is due for the time they are awake for the purposes of working, not for the time they are asleep or awake only for themselves. If they are expected to work for most of the shift and only nap between tasks, the whole shift can count. If no suitable sleeping facilities are provided, the whole shift counts. A listening ear while reading in bed, when they are allowed to sleep, is the example GOV.UK gives of time that does not count.
Working time, and the rota you publish
Whether the waiting time is working time for rest and the 48-hour week depends on how constrained the person is. That is a different statute from the minimum wage. GOV.UK itself separates the two when it discusses travel. Do not copy a minimum-wage answer across into a working-time answer, or the other way round. If the constraints are tight, read the working time guide and take advice before you decide the week was only the call-outs.
Shiftbrook can publish the on-call block as a shift, with a start and an end, so the team can see who is holding the phone. It cannot tell a sleep-in from a working night, and it does not pay the allowance or the call-out. If they are called in, add the hours that were actually worked before the timesheet is approved. The CSV is the record you take to payroll. The product does not decide that a night at home was, or was not, work.