Hang on a minute - "pelargonium" and "hardy" are not words you'd find in the same sentence. Pelargoniums are summer bedding plants commonly called geraniums, and need protection in the winter. Is that what you're talking about? If not, need to know exactly what plant you mean, or can you post a photograph.

Most Pelargoniums outside of P. x hortorum and P. peltatum (the tender species Bamboo is talking about) bloom only once a year in the spring, and will need a couple of months of cold weather to form flower buds again. This is especially true of the hardier species. I do have to agree with Bamboo in part though: even the hardiest species are likely to be somewhat tender in the UK. Are you sure it's not an actual species of Geranium?

Thank you Bamboo and Tugbrethi!
I've posted a photo of the pelargonium/geranium in question. As you can see, it actually does have one flower right now. Any thoughts on which it is?
I say hardy because it sits outside all winter unprotected, without seeming to mind.
Would one answer simply be to take cuttings and start again? Maybe it's just tired after (roughly) six years...

You're right, it is a pelargonium, but not fully hardy nonetheless. Presumably where it is over winter its out of the rain enough to keep it going - they will withstand up to ten degrees of frost, but what usually kills them is winter damp. As its been so successful, I wouldn't get rid of it - you say you've had it six years, I'd be inclined to give it a larger pot next spring with fresh compost, and feed it bi weekly with something like Miracle Gro general purpose liquid, double dose. That should get it to flower better, but don't feed it like that now if you want it to get through another winter!

Thank you, Bamboo - much appreciated! I shall do as you advise. I'd certainly rather try giving it a boost than abandoning it.

Because of the winter chill phenomenon, you will probably get your best bloom on stem tips that survive the winter, too. There probably weren't that many this spring!

Good point, Tugbrethi. If I had any sense I guess I'd give it some protection. In fact, I've just decided I will!