Speedwell plant, also known as Creeping Veronica.
It's an annual weed that spreads through lawns and borders, and has an attractive tiny blue flower. It spreads by seed in spring and autumn and there's two ways to manage it.
In borders... hoe it before it flowers and sets seed, then remove it.
In lawns... increase the height of the cut so that it is shaded out by the grass and ensure the sward is dense and healthy.
In lawns, spot-treat the weed using a weedkiller such as a 2,4-D-based herbicide in spring or early-summer, when growth is at its most vigorous. Repeat through summer where necessary. Apply in cool, moist, still conditions when there is least risk of the chemical drifting onto and damaging nearby garden plants.