No problem at all, North or South. There are quite a lot of mainland-registered cars in NI (some are bought secondhand from the mainland), as well as from the ROI. No border control whatever. Saw a couple of British foot patrols in Co Tyrone, including one roadside check, but that's getting rare. They still have some 'control zone' near army bases and police stations (still heavily fortified), where you mustn't leave a car unattended, or will be treated as security risk. You are still aware, though, if you are in a Nationalist or Unionist area of town/village (posters, flags, graffiti etc). No aggro at all, but lots of friendliness towards English visitors.
Alec