First I removed the sleeves, collar, bottom edge using a seam ripper but I then trimmed some more off with some scissors anyway to make it nice and loose around the neck and sleeves. I also trimmed the bottom so that all the edges matched.
But I decided to jazz the tank up and bit and I've had an idea for a while about lacing up a top with a shoe lace (I actually bought some dark orange cord- 2m for 80p). So I cut away from the sides of the T-shirt (first I flattened it, and folded it over so everything would be even and match up). Then I used the seam ripper to cut small holes along the new cut edge. And lace the cord through.
I'm pretty pleased with the effect, but it would have worked out better if I'd used a slightly bigger T-shirt (this one says L in it, but that's some kind of tiny alien large I presume), I think I'll try it again to make a tank for summer.