Although you've not specified clearly, from what you're saying you appear to be asking about Globe Artichokes rather than Jerusalem artichoke.
I'm sorry to confirm that longstanding recommended practice says you should have removed the small heads which form in the first year as soon as they appear, and not allowed them to develop to any size. However, not everyone follows that, preferring to crop from the plants as soon as they start producing if that happens in their first year, which is probably why you're finding conflicting information. The theory says regular cropping begins in the second year, when the terminal bud (king head) should be cropped, leaving 2 or 3 inches of its stem still attached to the plant - it should be large and swollen but still green and unopened. Fertilizer should then be applied after this initial cropping, and later in the season, remove and cook the smaller secondary heads. They should be cropped when they've developed well, but just before the fleshy scales start to open.
It's now late autumn in the UK, so the plants should be cut down (which will get rid of the heads you still have as well) and covered with something insulating, like straw, bracken fronds or leaves, horticultural fleece if you don't have those materials available, to protect them from frost.
You've come this far - if you can bear to keep the plants and try to overwinter them, then you'll be eating globe artichokes next year, seems a shame to give up now. If you haven't sufficient room, its possible, if we have a hard winter, that one or all of your plants may not make it through the winter, so why not cut them down, cover them and see what grows next year; if they all survive, you can perhaps remove one or two to reduce crowding. Whilst removing a leaf or three here and there does no harm, removing quite a lot of foliage through the growing season isn't a good idea, so it would be better to reduce the number of plants you have to try to avoid that. Best results are achieved by applying liquid fertilizer fortnightly throughout the growing season, from late spring onwards. For future reference, these plants can be grown as a normal border plant, in amongst other shrubs and perennials, provided you leave enough room for them - the recommended planting distance between one plant to another is 36 inches, so yes, I'm afraid they do take up a fair bit of space.
Having said all that, if the heads on your plants are a good size, might as well cook them and see what they're like to eat rather than just putting them on the compost heap,as you've left them on the plants and they're about to be cut down anyway - they won't get any more ready than they are now.
