Our DNA adapts quickly because the the environment has changed. In a sense in all species the mutation rate is constant, and if the environment stays the same then those changes are unlikely to be useful, so won’t be selected for, so there are very few changes in the DNA sequence that survive from generation to generation. However, in our case we’ve moved from Belgium to Orkney. So mutations occur at the normal standard rate, but as the environment has changed (it’s colder and wetter) some of the those mutations will be beneficial to us and are selected for and stay in subsequent generations. So our DNA adapts quickly, despite the fact that the mutations rate stays the same, as the change of environment means the type of selection changes.