You have to be a bit careful researching knee socks in large sizes, the main source of <ahem> adult-sized white knee socks are aimed at quite a different population. But the uniform4kids ones linked to above are properly big enough, ime. John Lewis also a good bet, but not tried online.
I've been buying navy knee-length M&S socks for my tall dd but, after only one wash, they're way too short. I seem to remember someone posting on here ages ago about a website that sells 'proper' long socks for school ............ does anyone have the details? Many thanks.