I've managed to fix it - I was using the wrong webservice for my needs! D'oh!
Here's the code for anyone who wants it:
$().SPServices({
operation: "GetGroupCollectionFromWeb",
webURL: siteURL,
async: false,
completefunc: function (xData, Status) {
$(xData.responseXML).find("Group").each(function() {
$("#WSOutput").append("GroupName: " + $(this).attr("Name") + "<br>");
});
}
});
(WSOutput is a standard DIV, and siteURL needs to be set up as an initial variable, using the format of http://site/subsite - I don't think a trailing slash is required.