Will my onions continue to grow?

At this time of year they are about ready to harvest. Let tops die down more - if weather stays good. Then fork them out and put them in a warm dry place to dry off for a couple of weeks. (greenhouse is good) then cut off most of the stems leaving enough to 'plait'them together, then hang (or put in box/crate - with airflow around them) up in a cool place. Consult your seed packet etc for how long they will keep. Then get eating!