I've been told that many UK newspapers will not review books that have already been published. Is this the case?
I'm not sure what you mean - how long ago are you talking? They usually publish books that are new releases - not much point promoting a book that isn't available to buy. National and large-circulation newspapers are extremely unlikely to review self-published books. Local newspapers might be interested in self-published books from local authors.
I didn't think they'd review anything unavailable at that minute either but I was told by a major PR company that that is their standard practice. The books would be published within 1 month or so.
Books coming out in a month would probably be available for pre-order, so that seems feasible. I'd imagine there's a pretty narrow window to aim for.
The big papers like the observer almost certainly get review copies send to them before they are available in the shops - as tenderiser said this will be the preserve of trad publishers, unless you have a personal connection or are famous for something else
You're probably looking at ARCs? Advance Review Copies? There's a pretty strong tradition of sending them out a few months ahead of publication so the review can appear on or very near the release date. I think it may be possible for self-publishers to sign up for NetGalley (which handles a lot of ARC distribution, at least for digital versions) but I'm not sure how you'd persuade journalists to select your book from the oodles available.