The responsibility for determining the number of councillors falls to the electoral officer of the district council, so a local council cannot alter its number of members. If more councillors are co-opted than the number of vacancies, the last person to be co-opted could not become a councillor. This doesn't invalidate the meetings held, but could result in many minor breaches of the legislation. This should not have been allowed to happen, there is really no excuse.
The resignation has addressed the numerical issue, but the person who was not validly appointed does not automatically become a councillor and the vacancy should be handled in the normal way, i.e. notice of vacancy, invitation to petition for an election etc.