Basically, "offence" is the correct spelling everywhere except the US.
It's an unfortunate offshoot of the great vowel famine of the 14th and 15th century (when the French took vowels from the British to use in words like "adieu").
While they were here, they took a load of consonants too...
This meant that vowels and certain consonants were in short supply when the colonists left for the new world and while they were able to obtain certain letter supplies from the indigenous peoples in trade for mirrors and beads, it didn't fully meet requirements.
In England we were able to grow more to satisfy demand for English, but some letters just didn't do as well in the new environment.
This leaves us with many differences (realise/realize, colour/color, honour/honor - and notably we have licence as a noun and license as a verb, whereas US residents use license for both purposes).