The sun’s temperature doesn’t change in a way that depends on the rotation of the earth. It does have a slow (11 year) cycle, but … I think that you’re referring to the time of the year when we feel the most radiation from from the sun.
For people living between the two Tropics (Tropic of Capricorn and Tropic of Cancer), this is when the sun directly overhead. But as England is north of the Tropic of Cancer, this never happens. So, the sun will shine most hotly on England when it is over the Tropic of Cancer, which is the Summer Solstice (so, this week – 20th or 21st June). However, this is hottest days are generally later in the summer because the earth need time to “warm up”, and because much of our weather depends not on the sunlight falling directly on us, but on the local wind patterns bringing cooler or warmer air.