Okay, this is all such good information, because bizarrely I have just realised that I haven't applied for a job a recruitment agency since I was temp-to-perming in the noughts. I've had them contact me about roles and also to help them head hunt.
Answers to questions - I freelance in a very niche UK industry with only six large corps (two of them are umbrella orgs) and lots of tiny indies - the job description is very specific in terms of area, title, job responsibilities and that it's one of the top six companies. I used to be in-house and reasonably senior but took a break after kids as it was too mental (both DH and I had crazy hours/schedules, not fair on kids etc)
@MuddleMoo yes it would be normal for recruiters not to say who the job is in the advert with if it's confidential (it's a one year contract, so if it was mat leave, they might not have announced that to clients yet, or if someone key is leaving and they need someone to hold the fort for a bit).
But, normally they phone you and say I have this job, do you want to know what it is, and obvs you say 'yes,' then they tell you as it's not the kind of industry where you could just swap in and out.
There only are two small recruitment agencies in this industry as it's so niche. It's not quite everyone knows everyone, but most key people know most key people. So you would absolutely definitely need to know the company and the job before you went for it, in case you know that you loathe the MD, or that their working practices don't suit you.
I would be really surprised if there was no job at all, but am so grateful people have suggested this, as it wouldn't even have crossed my mind! Absolutely crazy that people do this!