Most public libraries now allow you to log into the catalogue and make reservations, renew books (if no one else waiting etc) online. Then you can see whether there's a queue, where you are in it etc.
I live in London where every borough has its own library system and has its own rates on fines, reservation charges etc. So I use Islington which doesn't charge for reservations. Normally dp works in the central library building (but not the library) so I ask him to collect and return books for me, but at the moment he's only going in occasionally.
Most libraries will be part of a network across the local authority area and borrowing from another branch will be easier, cheaper and probably faster than inter library loans. My favourite library has an online suggestions option and it takes time but they've ordered a lot of the books I've suggested - I've tried to restrain myself to suggesting books that will be of interest to other readers too, and I think at least one must have been requested by other people as well as me as I was 3rd in the queue to borrow it by the time it showed up in the system.
As others have said, better ask now. If others aren't waiting, you can renew several times, and you can take books in to the library and get them reissued.
With series that were published a few years ago, if your library service doesn't have every volume in stock, and this can be a problem, it might be cheaper to buy secondhand online if the books aren't too expensive, or some series have been brought out on Kindle. Abebooks.co.uk allows you to see if you can buy several books on a series from the same seller as then the postage per book works out a lot cheaper.