Yes, in fact it was encouraged and there were coins specifically designed to make it easier to do. Those are typically called "long cross" pennies, and they're fairly common, depending on period. The English penny remains remarkably similar from its inception around the early 8th century until the Tudor period. Barring a few Early Medieval examples, the English penny typically bore an obverse portrait design - the "head" - surmounted usually by the name of the ruler in a ring around the edge of the coin, but could feature a wide array of obverse designs. In pre-Conquest English coinage, a similar edge ring on the reverse also bore the name of the moneyer responsible for the minting as a kind of trademark of authenticity, and, especially from Æthelstan's Rex totius britanniæ issue of the 920s onwards, the location of the mint as well. The rest of the reverse design could feature any number of designs; coinage minted in Chester by Æthelflæd between 907-920 is noted for its pictoral reverse designs celebrating the restoration of the Roman city, and "Manus Dei" depictions inferring a blessing. The Manus Dei makes a wider appearance during the troubled reign of Æthelred II. The most popular design, however, is typically a cross, or rood, most often surrounded by 'pellet' or 'lozenge' designs. Initially 'short cross' pennies, similar to a Maltese cross, these designs steadily move towards experiments in a 'long cross' design, with a design specifically intended to help in the division of the coin.

During the reign of Edward the Elder (899-924), the moneyer Heremod conducts some experiments in reverse designs that are specifically designed to allow the coinage to be struck into two equal ha'pennies 1009.0314 and 1020.0758 are particularly clear and well-survivng examples. Where the type really blossoms, however, is during the reign of Æthelred II, the 'Unready'. We have a pretty substantive numismatic corpus for Æthelred, in part because of the vast amounts he minted to pay off the Danes, much of which survived in hoards, but also because his reign, while beset by instability and invasion, was actually quite a long one. Æthelred really goes in for Long Cross pennies, and indeed over 2,600 surviving examples are included in the Fitzwilliam EMC Sylloge. Æthelred Long Cross types typically retain the outer band on the reverse detailing the mint and moneyer, but the disc is otherwise split by the arms of the cross into 4 (more-or-less) equal quarters. The arms of the cross are themselves split split by a central channel which is designed to make it easier to split the coin, perhaps if striking it with a chisel. 1065.0518, 1001.0676 and 1001.0686 are good examples of this design. Notice that while the grooves technically stop at the edge band, the bands themselves are also marked for easy halving and quartering. This design feature remains relatively common through the reigns of Cnut and Harthacnut, and indeed we have extant examples such as 1045.0216 of coins which have been struck into ha'pennies precisely by using these long cross channels as guides.

Long Cross pennies remain a feature of issues under Edward the Confessor, although the brief reign of Harold II in 1066 provides a surprisingly extensive corpus of pennies in which the reverse cross is replaced simply with the word 'PAX'. Perhaps a folorn hope, although examples suggest that in lieu of a cross, the central 'A' of pax was a helpful marker when dividing the coin. Although William I does keep a Long Cross design of a sort post-Conquest, the cross design is more floral in appearance and no longer breaches the outer band, making it less useful as a tool of division. 1020.1350 is a good example of this.

By the 13th Century, long cross pennies are back with a vengeance. As part of his significant numismatic reforms, Henry III introduced a new style of Long Cross in the 1240s. Unlike previous designs, this new Long Cross, seen clearly in examples such as 1200.0475 and 1200.0481 stretches the whole width of the coin, from rim to rim and cutting through the outer band. In this, it was actually a defence against fraud, as it allowed people to easily see if the edges of the coin had been clipped, which was by far the most prevalent means of fraud at the time.