Get a ball of string (see diagram).
Have someone hold one end of the string at the starting point while you walk due south or due north to the other location while holding the ball, letting it out as you go (see diagram).
Measure the string. If it is less than half the longitudinal circumference of the Earth the length of the string is the distance. Otherwise you went the wrong way and need to subtract the length of the string from the longitudinal circumference.
Alternatively you could convert the difference in latitude to radians by multiplying by then multiply by the radius of the Earth.