Your answer to this may depend greatly on when, where and also what you count as 'counterfeit.' Mid-late Anglo-Saxon coinage was, as a rule, quite tightly controlled and regulated, and new issues were fairly common. As a result, we have a fairly comprehensive numismatic record. Æthelstan's 'Grately II' legal codex contains harsh penalties for moneyers who were found to be fraudulent, namely that their hand be removed and nailed above their forge. This kind of disfiguring punishment is rare for the period and much more common in post-Conquest Norman legal codes, and so reflects the severity with which fraud was regarded. The type of fraud with which Æthelstan was concerned, however, wasn't the typical manufacture of imitation coinage, but rather coinage that was produced underweight, undersize or had been trimmed down by unscrupulous moneyers, pocketing the extra silver for personal gain. By the 970s, King Edgar became so convinced of the issue that he organised a major overhaul and renewal of the currency. Curiously, the numismatic evidence suggests that while the silver weight of English coinage had decreased on average between the 920s and 970s, the difference itself is actually quite minimal, and is unlikely to have had a major economic impact.

This stands in stark contrast to Carolingian France, where minting was 'farmed out' to local elites, with predictable results. The quality and weight of Carolingian coinage varied so greatly during the ninth and tenth centuries that it was actually confiscated at English ports to prevent it diluting the currency in circulation there.

There is some evidence of imitation coinage as well. During the ninth century, a small but steady supply of copies of King Ælfred of Wessex's London issue coinage appears from the South-Eastern Danelaw. This does not appear to have been an inherently criminal act, however, as the silver content of these imitation pennies is broadly similar to legitimate Anglo-Saxon coins, but rather either an active attempt by the Danish communities in England to integrate themselves into a burgeoning proto-English economy, or as a show of English loyalty by English moneyers living in the Danelaw.