Your right to a refund, in respect of a faulty item, only exists until the point when you're legally deemed to have 'accepted' the item. Basically, it gives you enough time to get it home and check that everything is OK. With some items, the 'pre-acceptance period' might be relatively lengthy (e.g. you might buy a car in January and not think to check that the air conditioning is working until the summer months). However, for most purchases, the pre-acceptance period usually only lasts a day or two. (By wearing the ring for several weeks, you've clearly shown that you've 'accepted' it).
Once the pre-acceptance period is over, you have no right to a refund. Your only right is to demand that the retailer (not the manufacturer) remedies the fault by either repairing the item or replacing it. (You can indicate which of these options you prefer but the retailer can substitute the alternative remedy if the cost of your option is clearly excessive).
Because you have no right to a refund, 'official' complaint routes (e.g. Trading Standards) may be of little use to you. If you want to jolt Ernest Jones into action, it might be better to let it be known that you intend to take your grievance to the press. (Most firms would rather lose �500 than face bad publicity).
Chris