The 30 day notice period is required in marriages which are performed under the Special Marriage Act. if a marriage is not registered, then it is not considered legal until and unless you can prove that the marriage took place following all the customs as required. hence if the solemnization has not taken place, then it is not considered as a valid marriage.
Her marriage before she married you is not legally valid since no registration took place however, you can file a case on the grounds of other proofs you have that she married him even if the marriage is not registered.
fraud case can be filed against her and her parents for suppression of the fact of earlier marriage but here you may face trouble since you acquiesced through your actions. your action would speak otherwise since you condoned her act.
Divorce can be filed on the ground of desertion since she refused to come with you to London. you may also take a ground of irretrievable breakdown of marriage. further, you have any proof with you that she asked for divorce stating that she doesn't need any money or alimony?