While at the beach I saw a very pretty wild plant growing in the
shingle/pebbles just above high water mark. It grows in a low (6") clump
of sprawling stems, and has glaucus blue ovate leaves about an inch
long, all the way along the stems. The flowers are at the tip, very
tiny, pink or blue.

I've never seen this before and have no idea what it is. Any suggestions?

Janet.