You will most likely spend less time admiring Stonehenge than it would take you to drive there from London. You will have to keep to the designated tourist path, never getting closer to the humongous rocks than a few dozen yards. There will be plenty of other visitors sharing the same path with you to make the experience somewhat less spiritual.
And yet, the scale and the mysterious nature of this prehistoric installation will undoubtedly make an impression on you. Whether you subscribe to any of the multitude of theories of its origin or not, the sight of those arranged rocks is among the most magical in the whole world.
UNESCO recognizes Stonehenge as a unique embodiment of our collective heritage. Hardly anything I can add to that.
I have not visited Avebury, about an hour away from Stonehenge (but the same distance from London). Its pictures on the web suggest a less impressive ensemble of megaliths, which likely explains its lower popularity. Those same pictures convey a more serene setting and possibly better close-up access, so something to consider in the future.