to be worried about replying for a job via an agency by emailing my CV.

[JustHowItIsToday]

I'm a freelance trainer and there's plenty of sessional work I'd like to apply for via agencies. But I'm concerned about giving out so much private information and worried about what will be done with it. Obviously I know not to put my national insurance number, bank account details, but I'll need to put past employers, qualifications etc or it won't be a CV.

AIBU to be concerned or is this just how recruitment works these days?

If someone had nefarious intentions, what could they do with your previous job information that could harm you?

There really is nothing to worry about, you are covered by data protection,
I would research the agency you want to apply to, make sure they are a member of REC then ring them, try to just use 1 agent if possible.

If you do decide to send your CV to an agency, make sure you specify that you do not want your CV sent out on a speculative basis. I always insist that my CV is sent only for specified contracts and that I have vetted the contract beforehand.