No. If an agency asks for payment for finding you a job, find another one. Recruitment agencies in the UK are paid by the employers for whom they provide suitable candidates. Usually the employer pays the agency a fee equivalent to a percentage of the new employee’s starting salary.
In the case of temporary workers, the employer often pays the employee’s wages to the recruitment agency, which then passes on an agreed rate to the employee, keeping a percentage for themselves. If you’re in this situation, be sure you know how much you’ll be getting for a job before you sign on the dotted line.
If you are negotiating pay directly with the employer, they may try to cover some of the cost of using an agency to recruit you by making you a low pay offer, so make sure you know how to negotiate your starting salary.