This is normal practice now if you are registering for temporary work. If your only registering for perm work they will not need your bank details.
Employment law has changed so much over the years that it is near impossible for an agency to work as an 'agent' any more. In the old days you were not 'employed' by either the agent or the client and your rights were very restricted. Today you almost always become an employee of the recruitment agency, they pay you, acrue holiday pay for you, deal with sick pay etc. and then invoice the company that they send you to. Because your their employee they have to ensure you have the right to work in the UK, hence you need an EU passport or a foreign passport and papers that allow you to work here. They also need to check out your NI number and it is much easier for them to set you up on the payroll at the same time, hence needing your bank details. So that everything can be checked out.
You would be staggered how many temps give false names, think they can get paid in cash (or a cheque that can be cashed) or want you to pay their money into someone elses bank account "because they don't have one", etc.