The usual cause of cloudy or milky water is air dissolved in the water supply. When pressure is released by turning on a tap the air comes out of solution in the form of many tiny bubbles that will clear from the bottom of a glass upwards. This is of absolutely no health concern, although it can make the taste of chlorine in the water more noticeable. The effect is usually temporary, perhaps due to a burst main, but if it persists you should contact Scottish Water.
If you are experiencing the problem but your neighbours are not, it may be that your internal or external stop taps are throttled, restricting the flow of water and causing it to become aerated. Checking that both taps are fully open may resolve the problem.