They might be hebe.....the dead stuff is not going to grow so you may as well cut it away...will give the live bits a chance to breathe and grow.....good luck!

Thanks Amblealic i will start snipping then.

They're both varieties of hebe. You've nothing to lose by cutting them back and hebes are pretty vigorous, so they'll probably shoot again. Hebe cuttings strike easily, so you could pop some shoots in a pot of compost, put an inflated plastic bag on top and place on a bright but not sunny windowsill. I've had prunings that rooted in the pile of debris to be burnt before I got round to having a bonfire, they're that keen to make roots.