According to my wife who grew up in England, September might be the best time of the year to vacation there. We went four years ago in September. We spend four days in London, and the temps were in the eighties each day with no rain. I can’t guarantee that it’ll be like that all the time. We’re going again next September, and we might not be so lucky.
Maritime climates tend to have their best weather in late summer to early fall, Ireland’s the same as is our Pacific Northwest.