It's probably an out of court settlement, so the people who paid don't have any recourse. It's common in lawsuits to send what's called a "demand letter", which is basically "this is what I want, if you don't do this then I'm suing you." The article isn't horribly specific, but it sounds like that's what these letters were. So paying it isn't an admission of guilt necessarily, but it's still a binding agreement.
Unless the law firm's conduct was so egregious as to invalidate the agreement (fraud, duress, etc), in which case the people who paid might have some recourse, but I don't have enough information to say if that's the case or not.
*Edit* - That's also all assuming that settlements work the same way in the UK as they do here. I really have no idea if that's the case or not.