From the 900s up until 1279 half pennies were generally cut coins, as were farthings. Although some extremely rare halfpennies/farthings are know to exist of a few issues notably of Henry II and III. But it appears they weren't issued in any great number, or if they were then very few have survived.
In 1279 with the recoinage round halfpennies and farthings were introduced (or reintroduced since they had existed sporadically prior to the mid-900s), and from then onwards there were three coins of the realm. 1d, 1/2d & 1/4d. In the 1330s they were joined by groats (4d) and halfgroats (2d), along with gold coins valued at 80d, 40d & 20d respectively.