What are the travel rules for EU citizens with (pre-)settled status travelling between the UK and Ireland, Isle of Man, Guernsey or Jersey (the Common Travel Area CMT)?

You will not pass through any immigration control when you enter the UK across the land border between Ireland and Northern Ireland, so you don’t need any documents to enter the UK on that route.

However, you may be asked to show your passport (which should be valid for the whole of your stay) or identity card to enter Great Britain when travelling from Ireland if you are encountered by Border Force.

Full details at https://www.gov.uk/guidance/travelling-between-the-uk-and-ireland-isle-of-man-guernsey-or-jersey

IMPORTANT NOTE - If you want to travel with an ID card rather than a passport, your EUSS status application must be attached to your ID card