Ask a glider pilot about the weather!
The normally positioned high doesn't pull air in from the continent - it pulls it in from the N Atlantic/lower Arctic regions. In the winter this is very cold.
In the summer this air is cool as well, so to start with in summer highs we have cool air but bright sunshine = feels warm in the sun, cool in the shade. These are the days glider pilots live for.
If the high stays in place in the summer, the inversion gradually lowers (don't ask me why, but there is met theory to explain it). The inversion traps the air close to the ground and stops it mixing with the upper atmosphere, thus dissipating its heat. That air is warmed each day by the sunshine, and gets hotter and hotter. A few days into a summer high it's hot in the shade as well as in the sun.
As an example, on the first day after a cold front during a summer high the convection will go well above 5,000 ft, with gliders to the thermal tops. If the high sticks and no cold front comes along, the inversion can drop to as low as 1,000 ft of warm sticky air - thermals don't go above it, glider pilots become bad tempered along with the rest of us.