Yesterday (1st June) marked the start of meteorological summer (and the high temperatures last week were hot enough for some and enough to last the year!)
At the moment, the GFS thinks the first 10 days of June are looking unsettled and changeable, then slightly drier/warmer towards the end of next week but the unsettled theme still continues until the middle of the month.
Thoughts from Netweather (from a few days ago) and TheWeatherOutlook on what summer might have in store for us.