A lot of the time, agency contractors don’t need to worry about paying their own tax as it will typically go through an umbrella company.
If you work through a recruitment agency as a contractor in the UK, the chances are that your recruitment agency has a relationship with one of the many HMRC umbrella companies like http://unifiedpayroll.co.uk/. You’ll usually see their name on your paycheck as they’ll be the ones paying you.
Before you get paid, your agency will contact the umbrella company to let them know the number of hours you’ve worked. That umbrella company will then invoice the client and handle all the administrative tasks, including calculating the tax and national insurance payments due to HMRC. They’ll deduct any relevant expenses, pay the appropriate tax, and then pass on the remainder of your income to you.
They’ll also usually take a cut of the pay themselves to compensate for their administration overheads and make a profit.