Two weeks before - dealing with leavers and withdrawals from the accepted Year 7 places.
Two weeks after - dealing with no shows, tracing those who haven't turned up as normal, making file requests, chasing electronic requests, setting up user accounts, adding to messaging accounts and sending those out, doing FSM checks, trying to trace the ones where a previous school wasn't declared, receiving file requests and transfer requests, dealing with people phoning up asking if there are spaces or how to apply for 2028, FAP admissions, offering further places, getting shouted at, filling in reports for every single one that's left and started, dealing with statutory changes, creating new records for schools that have changed names or academised, having repeated calls and emails from people who are chasing a response - oh, and doing the other parts of their jobs, as they won't only be employed to do Admissions.
If they are fulltime TTO, you're actually talking about them being able to do all that in what could be less than ten days, assuming the council took their usual length of time to provide the in year list. And if they're, like most support staff, only on a part time contract, even less time.
Yes, it's frustrating and worrying, but there's only so much that can be done.