Not a100% but i think that there is a timescale of 5days with BT certainly would apply to BT retail for telephone, they basically will aim to repair a fault within 5 working days, if it takes longer then they pay comphensation for the time you are without a service,
I would of thought that your isp would have not continued charging the monthly fee after the 1st month of no service, what min term contract are you on 12mths or a rolling 1 month? If it where me regardless of the min term i would of stopped the monthly payments by now, but in your case if they won't refund you/credit your account once this is fixed,
Have you discused the taking of monies for a service that isn't being provided with Vivaciti ?
I would make an official complaint to their ADR letting them know that you want refunding for the whole period you where without a working service,