There were a few, but not enough. Archers were available to the Saxons at Hastings. While present at Stamford Bridge, the lightning rush south meant that few made it to the battle. Even in the latter Middle Ages when the English archer ruled supreme, they were rarely wealthy with access to horses. In his haste to meet William in battle, Harold was forced to leave them behind and didn't delay in London long enough for others to be raised. As a result, the Normans were strongest where the Saxons were weakest, in mobile cavalry and archers.