In 1925, English antiquarian Alfred Watkins published The Old Straight Track which proposed that significant English landmarks - such as chalk carvings, henges, hill forts, Roman and medieval sites etc - line up along straight lines across the country and lines could be drawn on maps between several of them. He supposed that these 'Ley Lines', as he called them, were the remnants of trackways used by ancient Britons. Archeologists dismissed his theory because there was no reason why the population at the time would travel in straight lines across hills and rivers etc, nor would they have the means to measure it. Watkins had also included things from disparate and unrelated time periods just because they happened to fall on his imaginary lines. Despite the rejection by archeologists, the principles of Ley Lines was picked up by a small but enthusiastic group of enthusiasts until it faded into obscurity in the 1940's.
Enter the 1960's counterculture. UFOlogists and spiritual seekers of 'Earth energies' (?) picked up Watkin's theories and applied them to their own beliefs. The lines became tracks followed by UFOs or they were ancient mystical lines known to the sacred druids; other proponents thought they were lines of energy that could be tracked using dowsing rods and still others thought the power of the lines could be tapped into to herald the Age of Aquarius. Needless to say, proper archeologists still thought it was all bollocks.
The reason for the supposed straight lines between various points on a map of Britain is simply because the number of archaeologically significant sites to choose from in this country is huge. In a random distribution of dots, the more dots there are, the more likely you will find some points that line up nicely in a straight line. Similar lines have been drawn on maps of pizza restaurants in London or using telephone boxes in the capital. Watkins was wrong but his ideas were grounded in reason - he hypothesized that the lines were simply roads that people followed for convenience - but the counterculture explanation is doubly wrong given that it is offering an explanation of something that doesn't even exist using things that also don't exist.