A few British equivalents for U.S. yarn weights:
3-ply is similar to U.S. sock weight or fingering yarn;
4-ply or double knitting is similar to U.S. sport yarn (the U.S. has been adopting the DK designation recently);
8-ply is similar to worsted.
(Please, Brits, correct me if I'm wrong.)
It becomes very confusing because the number of plies (individual threads in a yarn) has little to do with the yarn's weight. 8 plies of fine silk can be thinner than 3 plies of loosely spun wool.
It would be nice if there were global standards for yarn weights. In the meantime, your best bet is to look at the gauge (number of stitches per inch) for any given yarn, rather than its weight designation.