The difference between UK and some European countries (so potentially Croatia too) with regard to tow bar is that some European countries require that towbar (apart from authorised installation) is checked by their equivalent MOT station and then relevant note included in the car registration document that the car has aftermarket towbar fitted.
No such requirement in the UK (whether before or after Brexit) hence OP has nothing to worry once they get their towbar installed.
No such requirement in the UK (whether before or after Brexit) hence OP has nothing to worry once they get their towbar installed.