Hi, Fiona,
Sorry for the delay in my reply.
While this part of the
Government website can be confusing, it highlights the same guideline we have on Ireland.com.
Entering Northern Ireland via the Republic of Ireland, there is no immigration control so your ID card is sufficient.
On the other hand, if you are looking to travel to Great Britain from the isle of Ireland, which involves taking a plane or ferry, you will require a passport as travel with an EEA or Swiss national Identity card is not allowed.
"You cannot use an EEA or Swiss national identity card to enter the UK, and can only use a valid passport" only refers to direct travel to the UK - including Northern Ireland - as there is immigration control when arriving directly to the UK by plane or ferry. Know that there is also exception here, which are listed on
the Irish official site.
I hope this helps clarify the information.
Elodie