The staff at Jobcentre Plus actively seek to get unemployed people to send their c.v. 'on spec' to potential employers. So there's no reason (other than the ever-mounting cost of postage) as to why you shouldn't give it a try.
If you can find out the name of the relevant person it would, of course, always be best to use that name when starting your letter. Otherwise, one possible way of starting the letter might simply be to head it "For the attention of the Human Resources manager".
You'll probably get very little response. (My own experience of applying for jobs is that fewer than 1% of employers ever reply to job applications, even when those applications are in response to advertised vacancies). However you might just 'get lucky'. A young friend of mine had completed the first year of his plumbing course at college but he couldn't continue with the course unless he could find a placement with an employer. I helped him to write, 'on spec', to 51 firms. 47 didn't reply. 3 sent back very nice letters apologising that they couldn't help him. But just one (which was all he needed) offered him a placement. Perhaps you'll have similar luck?
Chris