I don't know though it seems quite a few publishers like authors to subsidise the costs.
I am an editor for the 6th largest academic publisher in the USA (Cengage Learning). I can't talk about how things are done in the UK.
I can tell you, however, that no legitimate US publisher will ask authors to put up one dime of costs. The standard industry publishing agreement is for an author to receive a royalty on net sales, and then usually to get a small advance on those sales. The terms on which that advance is payable, or if there is an advance, is negotiable (some authors, for example, forgo any advance for a higher royalty—especially if they already wrote the book before signing with the publisher). But the publisher subsumes the costs of publication. That is the entire reason that the publisher can legitimately claim the lion's share of the profits. The publisher is taking all the risk, putting its own money into the printing, marketing, distribution, and so on.
Any situation in which you are paying someone else to print your book is simply a marketing/distribution deal. You wrote the book, you print the book, and rather than paying an independent marketing firm up front to market and distribute your book, you're paying them a royalty. If you're going to do that, you better be very sure that they have a very solid marketing, distribution, and sales record. Otherwise, you will have paid thousands of dollars to print a lot of books that sit in your closet (or a warehouse).
Honestly, If your book doesn't find a traditional publisher, I think you'd be far better off going the self-publishing route with Print On Demand and eBooks than paying thousands for a huge print run and giving up royalties. I am in the process of writing fiction myself, and I plan to do exactly that if I cannot find a reputable US publisher.