No, agencies cannot charge you a fee for taking you on their books, for searching for work for you or finding you temporary work. They can charge for some other services that they provide, such as providing accommodation, transport services, help in preparing CVs etc., but they cannot require you to sign up for these additional services as a condition of finding work for you and shouldn't put pressure on you to do so.
The agency or employment business must give you a key information document (a short document, no more than 2 sides of A4) setting out the key features of your relationship with them, including, in particular, any fees and other deductions and a realistic estimate of your takehome pay.
If you do sign up for additional services for which the agency makes a charge, they must confirm details of these in writing, and inform you of your right to cancel or withdraw from the service by giving five working days' notice (ten working days' notice is required to cancel accommodation services only). Your agency cannot require you to provide a longer notice period.
You should not be penalised for giving notice to end these arrangements, e.g. by having an assignment terminated, being refused future assignments or being offered assignments on less favourable terms.