I have just been assured by "the country's biggest recruitment agency"
that it is normal practice for agents to need referees but refuse to
say who the client is.

All the advice here has been not to fall for this trick.  So I
declined.

The agent was adamant that this is how it contractor recruitment works
"I think you'll find it is the same with every agency".

The explanation was that because they are the sole agency (the client
is supposedly "a local authority" - since when could the public sector
use just one supplier for recruitment?) I don't need to know who the
client is and that it is normal in consultancy to not reveal your
clients.

Can someone please confirm: is it me that is in the wrong?  Should I
have provided the referees details without knowing who the client is?