Thank you to everyone who made helpful suggestions re book-storage - I thought rather than replying to the comments, I'd write another post, as they may be helpful ideas for the rest of you (many of whom confessed similar dilemmas), before sharing my answer! The problem has proved only more pressing in the last 24 hours since the arrival of a stash of VMCs...
1. Billy bookcases from Ikea are very popular; I like the idea but I can't afford to replace my existing cases.
2. Install brackets above bookcases - this would work if we weren't renting!
2. Refrain from having children as they are likely to be an exacerbating factor as they accumulate their own books. Luckily I do not have maternal instincts.
3. Culling books. This invariably leads to regret, as several people have admitted. I am quite good about this and do get rid of books that I don't want to keep; unfortunately since discovering the Notting Hill books and comics exchange I invariably end up with as many books as I have got rid of.
4. Boxing up books - putting them into storage, or under the bed. No space under my bed sadly (that is where I keep my shoes), and although we have a storage unit (where K's books are currently housed), I prefer to have my books where I can see them... I do have a catalogue of my books on librarything which helps in the organisation of them.
5. Act as a lending library. I think this suggestion was made in jest, but actually I have resorted lending books to my friends and family, particularly new acquisitions, so that I don't have to find them a home.
6. Store books at your office. I do have 2 shelves under my desk where I often keep books that I am lending people/borrowing from others (Stuck in the book and I regularly use it as our exchange place...); there is potential to extend this but I don't think it would be quite right!! I do have a locker which I could utilise better...
7. Double/triple backing books. Sadly this doesn't work too well on my shelves as they are not very deep, although I do put books which are awaiting culling behind my regular books - it is very difficult to get them out though and as I said above, I do like to have my books on display!
8. Borrow books from the library. I do already do this and borrow books at a rate of knots (I estimate that I take out and return 20 books a week, but I don't have the physical capacity to take anymore, plus there is the availability issue - lots of my VMCs are not available from the library).
Lots of good suggestions - many thanks readers!
So what has my solution been? We identified that if we didn't mind restricting our access to the kitchen slightly, we could replace one of the small bookcases with a tall one (which will also have room for another row of books on the top). It's still in construction here you see, but I have Friday off and hope to rearrange all of my books then!
We also found that if we turned the dining table through 90 degrees, and don't mind sitting side by side staring out of the window while we eat (this may not last, as our 2nd floor flat overlooks a busy road and bus route and I'm not sure how much we'll look like we're in a zoo), there is room to fit in the small bookcase AS WELL. (It obstructs a plug, but hey - who needs to hoover the dining area?!).
Finally, I am bidding on a small revolving bookcase on ebay, which could sit next to the television.
I hope we will have found a house before these things are filled up. K says that if it has a garage he will convert it into a home library for me...