the first person you should complain to should be the practice manager at your dentist. she/he might be able to sort things out for you without you needing to take the case further (ie, offer to pay for your further treatment/refund you etc).
if that doesn't work out you could then take the case to the gdc, but this will *never* get you a monetary resolution, this is just about whether or not your dentist has been negligent and if she/he is 'fit to practice' - your dentist can be given a warning or prevented from working as a dentist if you 'win'.
if you want a financial resolution and you don't get it from the practice manager at your dentist, i think the only way is to sue your dentist and there are law firms specially dedicated to this (you can google them under 'dental negligence' and they tend to take cases on a 'no win, no fee' basis).
but, i really think it's best to try with the practice manager first. the gdc is a long route (which i've been down myself) and it's worthwhile to do if you feel you've been treated badly but it takes literally MONTHS for all the evidence to be heard, decisions made etc!!!