Am I employed or self-employed if I work through an agency in construction?

It depends on your actual working arrangement, not what your contract calls you — if the agency or contractor controls how, when and where you work, provides your tools, and you can't send someone else to do the job for you, HMRC is likely to treat you as employed for tax purposes regardless of what label is used.

Genuine self-employment means you carry your own risk, can be substituted, and control how the work gets done — which is common for subcontractors on CIS but not universal. Getting this wrong matters: if you've been treated as self-employed but HMRC decides you should have been on payroll, the contractor can end up liable for unpaid tax and National Insurance, and it can unwind retrospectively. If you're working through an agency and aren't sure which side of that line you're on, it's worth having your specific arrangement checked rather than assuming the paperwork settles it.