The Advantages
Working on an assignment through an Agency is a common activity for labour only contractors or consultants. The easiest payment structure is to become an employee of the Agency for the duration of that assignment. Like any employee the worker will be paid under PAYE, the Agency will not be charging a fee and should support all normal employee statutory rights such as holiday pay. For short term assignments, where there are no expenses to be claimed, this is probably the right choice.
The Disadvantages
Smaller agencies often do not have a payroll department. Moving from Agency to Agency as assignments change can be a problem. With changing assignments there is no continuity of employment or self employment to support mortgage applications and other credit related enquiries. Agencies do not generally pay tax deductible expenses. Generally those who qualify to work legitimately on a self employed basis pay significantly less tax than Agency employees.