Now a clause that should actually deliver some money!
The Publishers shall make up the account for royalties on copy sales of the Work at December 31st in each year and deliver the amount due to the Author within 3 (three) months thereafter provided, however, that no account need be submitted unless specifically demanded nor payment made where the amount due is less than £10 (ten pounds), in which case the amount will be carried forward to the next account.
This means the publisher will pay you once a year, by the end of March, for the money earned on royalties over the previous year. This is a bit ropey, as many publishers pay royalties twice yearly, in June and December. Or, rather, they actually pay in March and September royalties earned to June and December. So - the publisher has your money for up to *15 months* without paying any interest and with no obligation to tell you how much of it there is. This is how publishing has always been. Starting from here, if this is your first book, you are likely to ask why they can't pay sooner, or issue more frequent statements. After all, it is no longer a matter of clerks in fingerless gloves adding up columns of figures Bob-Cratchit-style. It is now a case of Excel spewing out data the publisher probably doesn't understand and is reluctant to pass on. But the very fact that The Bookseller can produce an analysis of half-year sales for the whole publishing industry to 30 June on 9 July, suggests there is no good reason why we should not know our sales figures more quickly. Rant over. It's not about to change quickly, so either enter a fruitless argument in the hope that if enough of us do so the publishers' resolve will eventually be worn away, or live with it and take out a bank loan. (Or don't - as you don't know how much you will get or whether the publisher will go bust before paying you.)
If you haven't earned more than £10 in royalties they don't need either to tell you or pay you what they do owe you. Instead, they save it for next year (no interest, of course). Not telling you is, I think, discourteous and probably a false economy. If you are diligent enough to notice they haven't got in touch, it will probably cost them more to process your queries than it would have cost to send an email saying there are no royalties. Maybe they should just give everyone £10 anyway to avoid the question :-)
Why does it take three months for them to extract a figure from Excel (which we know is available the first working day after 31st December) and convert it into a computer-generated royalty statement with errors in and a BACS transfer (minus the VAT, which they will have forgotten to pay again)? Because they can get away with it. If you want to argue this one, cite the fact that PLR - paying many, many more authors than any single publisher - gets their payments out a few days after sending statements in January or early February and these are also calculated to 31st December. It's something we should argue against, but frankly there are more interesting fights to have. Once you are used to the fact that royalties are paid in March (and September, usually), it still happens every 12 (or 6) months so it doesn't hugely matter. And as for the fact that they can earn - or save - interest on your payment for three months, well, it might just keep the publisher solvent, which will benefit everyone.
My advice regarding this cause depends on the rest of the contract. If the publisher is trying to get any electronic rights, point out that if their understanding of technology is so rudimentary that they think it takes three months to calculate royalties and make a bank transfer, they are not a fit custodian of any type of electronic rights.