Met Office meteorologist Craig Snell said Sunday “started on a sunny and bright note for a lot of the UK” as clouds moved in over Northern Ireland and western Scotland.
The area of cloud and rain is set to spread eastwards and limit the sunshine.
In an online forecast, he added: “The heaviest and most persistent rain will be across parts of Northern Ireland, southern Scotland and northern England and for all of us it will be a windy afternoon.
“Potentially come the end of the afternoon we could just see some gales along the Irish Sea coast.
“And with the cloud, wind and rain combined, for most of us it can be feeling fairly chilly for the time of year.
“But down towards the south east where we hang on to the sunshine for the longest we will just climb up to about 20C or 21C.”
Following the bank holiday weekend for England, Wales and Northern Ireland, warmer conditions are expected to develop during next week in central and eastern areas, with the possibility of some hot weather for a time.