Hmm, would have been good to have a photograph - there are annual cornflowers (meaning they grow, flower, set seed and die in a year) and perennial ones, and I don't know which ones you've got. If the seeds you bought were listed as Hardy Annuals, then its likely that's what you've got and they can be taken out.

Hi, welcome to GoY, I agree with Bamboo, they're more than likely hardy annuals, but that doesn't mean neccessarily, that you've seen the last of them, if you didn't dead head them they will more than likely have scattered seed, which will germinate next spring, Derek.

Thank you gents. I will attempt a photograph tomorrow. I didn't do anything to them during the year, but they seemed to grow very tall which made them unstable in windy conditions. They still have some rather poor flowers, however if I can do the picture tomorow then perhaps you can confirm what they are and what it would be best to do.
My gardening expertise is such that all I did was go to B&Q and pick some seed packets with pretty pictures of colourful flowers, however with the exception of a couple of nasturtiums only the cornflower seems to have come to anything.

One gent and one female, by the way! If they got tall, with flowers on top, and didn't have a bushy, basal clump of jagged edge leaves, they're likely the annual type, not perennial.

Oops, obviously I was Bamboozled by your name!
I have submitted a photo today however I do not know if it will be clear enough for it to be of any help.
I have not yet fully understood this site, so I do not know where the photograph has disappeared to as unfortunately it does not seem to be possible to simply attach it to this comment, however as I type this a small version of it has appeared above, so I assume you may be able to access it from there.

Its under photos on your profile page, and it does seem they're annual cornflowers rather than perennial.

Thank you. So I just take them out and start again next year?

As Derek said higher up in the thread, you might find they seed themselves anyway - the trick is to recognise them when they're small as they pop up next year rather than weeding them out. And yes, you can clear them away now if you want to, and sow more next year too.