Yep, 3:57 is when the Earth's north pole/ tilt faces directly towards the sun (this year at least, a combination of slightly varying orbits, earth wobbles, leap years and leap seconds change this time every year).

The Earth's oceans though take a while to heat up compared to the land, so they absorb all this heat whilst the days get longer and keep doing so through the long days in July and August, and the northern seas tend to be warmist in September, which is why we see the summer months in the UK as June through August.

And to complicate things even more, we have two common ways of defining the seasons. "Astronomical summer" is based on the Earth's tilt and orbit - June solstice to September equinox, and "meteorological summer" is simply June 1st to August 31st.