Drowning in admin after going from 3 to 12 staff

We’ve had some decent growth over the last 6 months, expanding from just 3 of us to a team of 12 now. The problem is that my Fridays have completely devolved into chasing people down for timesheets, manually checking holiday requests, and trying to make sure I don't mess up the HMRC submissions.

We are currently doing everything through a mix of generic spreadsheets and basic tracking apps, but it’s becoming a massive bottleneck. One wrong tax code or missed overtime calculation throws off the whole week, and honestly, I don't have the time to become an expert on payroll compliance while trying to run the actual business.

I’m looking for a proper UK-based setup that integrates both the time tracking and the actual payroll processing in one place so I can stop copying data back and forth. Ideally something flexible that doesn't force a small company into a rigid annual contract right away. How are you guys automating this transition once you scale past a handful of employees?