The air above about 3000 feet the last few days is very warm and dry and if the cloud disappeared the temperature would shoot up rapidly to about 28°C. But the lower layer of air is cool and moist and cloud can't penetrate the warm air, being cooler and therefore denser. So if the upper air were cooler there'd be some chance of the cloud being carried upwards and evaporating and we'd have a warm, sunny day. Maybe not 28°C but at least 23°C. BTW the sudden rise of temperature as you go up above about 3000 feet (in this case) is called an inversion and is a common feature. In Siberia in winter it can be as much as 25 degC warmer aloft than at the surface, say -20° compared with -45°.
I'm working from home on a Saturday, trying to get stuff done before going on holiday for two weeks in a fortnight's time. But it's an opportunity to go through my CD collection one-by-one as I work. I hadn't unpacked them since I moved here almost a year ago. Right now: CD 3 of the complete collection of Vaughan Williams symphonies.