When you say "solar time" you of course mean "mean solar time" as solar time is very different from mean time.
The day in (northern) midwinter is about a minute longer than the day in Summer, because the Earth's orbit isn't round, so solar time falls behind mean time and then catches up again. Of course no one noticed that until reasonably accurate clocks appeared, but clocks (and the atoms behind UTC) keep mean time rather than the slightly fluctuating solar time, since the length of a day, minute or second doesn't depend on the angular velocity of the Earth at a particular point in its orbit, just on the period of the inbuilt oscillator (pendulum, crystal or atoms).
So clocks and sundials don't actually keep the same time, and a well-made sundial will have additional markings to tell you what correction to apply at various times of year to convert to clock (mean) time. "Watch faster" and "Watch slower" are the markings I have seen.