You mean pre-crusade England?

In pre-crusade England there was no (modern) English, but there are several Latin words that have this semantic sense.

• parracida literally means murderer of a relative, but as a head of state is kind of the ur-father, the term can mean assassin.

• sicarius is a murderer or an assassin

• interfector (fem: interfectrix) is a killer, murderer, assassin, destroyer

In Old English, they could simply be called a murderer. (morðorslaga, morðorwyrhta, etc)

'Murder' originally had another meaning in Anglo-Saxon and other Germanic cultures, distinct from just killing, the word 'morðor' implied that the killing was done secretly, in a cowardly or treacherous way such as through poison or witchcraft. Killing someone in the open was a less severe crime, if you took responsibility for it, payed the weregild and so forth. Secret killing, on the other hand, was a death sentence. For instance, the Laws of King Æthelstan:

And we have ordained respecting witch-crafts, and lybacs, and morthdaeds [acts of murder; secret killings]: if any one should be thereby killed, and he could not deny it, that he be liable in his life.

The term 'murder' has broadened in other Germanic languages as well, so their terms for 'assassin' have added an adjective: Meuchelmörder ('cowardly murderer', German), sluipmoordenaar/snikmorder ('sneak murderer', Dutch/Norwegian), launmorðingi/lönnmördare ('secret murderer', Icelandic/Swedish).

So it's not that they didn't have a word, as much as the broadening of the existing one that required a change. If the Normans didn't come along, the word for 'assassin' well have been 'sneakmurderer' in English.