Need packing advice for upcoming overseas trip

I am going on a cruise of the UK at the end of May. For when we are on the water I am packing warmer clothing (1/4 zip pullovers, sports coat). For walking around during the day in Belfast, Inverness, Dublin, Liverpool, Dover, etc… should I plan on short sleeves or shorts or bring a jumper or light rain jacket? Any suggestions from the locals would be appreciated. Thanks